Hi and welcome to this video about Standard Temperature and Pressure! In this video, we’ll review what pressure and temperature are and discuss what scientists and engineers refer to as Standard Temperature and Pressure. Let’s get started! Show Even if you aren’t familiar with the exact formal definition of pressure, you probably have a good idea of the concept. When something pushes on your skin, you feel pressure. When you apply enough pressure to a filled balloon, it pops. But what exactly is pressure? Pressure is defined as the amount of force applied per unit area. This should be pretty intuitive if we look at the example of something pushing on your skin. The object, let’s say a fingertip, applies a force to the skin on your arm and only does this over a certain area of skin equal to the size of the fingertip, applying pressure. It’s important to note that pressure is a scalar quantity and is not defined as having a direction. There are a couple of different equations for pressure. The first is simply the definition of force (F) per area (A): \(P=\frac{F}{A}\)It may not be as obvious, but gases can also exert pressure. For gases, pressure is discussed in terms of temperature, volume, and the number of gas particles, and for this, we use the ideal gas law: \(PV=nRT\)In this equation, P is the pressure, V is the volume, T is the temperature, R is the ideal gas constant, and n is the amount of gas in units of moles. An example of gas exerting pressure is the pressure from our atmosphere, referred to as atmospheric pressure. Our bodies are used to and even rely on this kind of pressure, so we don’t feel it in the way we would if something were pushing on our skin. Atmospheric pressure exists because the gravity from Earth holds down various gases that make up the atmosphere. This pressure increases the deeper you go below sea level because the amount of air above you increases. At sea level, we say that there is 1 atm of pressure. However, as we climb up to higher and higher ground, we experience less and less atmospheric pressure because there is less and less air above us. This change in pressure is why our ears pop with changing altitudes.  1 atm of pressure is equivalent to about a 10,000 kg mass pushing down on a square meter area. We can think of all that mass existing in a very tall and thin column above the surface. The atmosphere is denser near the surface and thins as the distance from the Earth increases. In this image, we see that 50% of the atmospheric gases exist within 5.5 km and 90% within the first 16.5 km. Above that, gases become very thin, and due to less available oxygen, it becomes harder to breathe. Now let’s go the opposite direction. Water is fairly heavy and there is a notable increase in pressure as you go deeper and deeper under the water. In fact, for about every 10 meters you go down, the pressure above you increases by about 1 atm. Now that we’ve got a better understanding of what pressure is, let’s talk about temperature. We all know that temperature measures the hotness or coldness of something, but how? Temperature is a measurement of the kinetic energy of atoms or molecules in an object. So, when we are measuring temperature, we are measuring the amount of energy in the molecules of the object. As the object cools, it loses this heat energy to its surroundings. Most everyday thermometers give a temperature in units of degrees Fahrenheit or degrees Celsius. However, the SI unit of temperature is Kelvin. Most scientists use this unit for temperature in their models and equations. It is a convenient unit, in part, because absolute zero – that is the lowest possible temperature – is 0 K. At 0 K the atoms or molecules of an object are completely still. When two objects of different temperatures come into contact, the higher energy particles (the hotter particles) will give energy to the lower energy particles until they all reach thermal equilibrium. In other words, the heat will spread out evenly until the two objects are at the same temperature. An example of this would be when your cold hands are holding a hot drink. Over time, the heat from the drink will warm up your hands and the drink will cool off. Scientists and engineers often use a set of conditions referred to as standard temperature and pressure or STP. Standard temperature is defined as 0° Celsius (32° Fahrenheit or 273.15 K) and standard pressure is defined as 1 atm of pressure. These values are used to describe things like properties of different gases. Since some properties can change with temperature and pressure, it is useful to have a standard temperature and pressure with which to compare these properties. Now that we’ve learned all about temperature and pressure, let’s check our understanding with some questions! 1. If you have a certain amount of an ideal gas contained in a rigid box (the volume can’t change), and then you raise the temperature inside the box, what will happen to the pressure in the box?
The correct answer is A. If we look at the equation PV = nRT, then we can see that when the volume and amount of gas are constant and the temperature is raised, then the pressure must also increase. If one side of the equation increases, the other side must also increase here. Note that temperature and pressure are dependent on each other. 2. If we assume the gases that compose the atmosphere are all contained within an altitude of 44 km, which statement most accurately describes the pressure at an altitude of 22 km?
The correct answer is C. The majority of the mass of our atmosphere is contained within the first 20 km of the atmosphere and the rest is quite thin, so by the time we get to 22 km, the pressure will be much less than half of the total. Less mass above you equals less pressure. That’s all for our video on standard temperature and pressure! Thanks for watching and happy studying!
By the end of this section, you will be able to:
During the seventeenth and especially eighteenth centuries, driven both by a desire to understand nature and a quest to make balloons in which they could fly (Figure 1), a number of scientists established the relationships between the macroscopic physical properties of gases, that is, pressure, volume, temperature, and amount of gas. Although their measurements were not precise by today’s standards, they were able to determine the mathematical relationships between pairs of these variables (e.g., pressure and temperature, pressure and volume) that hold for an ideal gas—a hypothetical construct that real gases approximate under certain conditions. Eventually, these individual laws were combined into a single equation—the ideal gas law—that relates gas quantities for gases and is quite accurate for low pressures and moderate temperatures. We will consider the key developments in individual relationships (for pedagogical reasons not quite in historical order), then put them together in the ideal gas law. Figure 1. In 1783, the first (a) hydrogen-filled balloon flight, (b) manned hot air balloon flight, and (c) manned hydrogen-filled balloon flight occurred. When the hydrogen-filled balloon depicted in (a) landed, the frightened villagers of Gonesse reportedly destroyed it with pitchforks and knives. The launch of the latter was reportedly viewed by 400,000 people in Paris. Pressure and Temperature: Amontons’s LawImagine filling a rigid container attached to a pressure gauge with gas and then sealing the container so that no gas may escape. If the container is cooled, the gas inside likewise gets colder and its pressure is observed to decrease. Since the container is rigid and tightly sealed, both the volume and number of moles of gas remain constant. If we heat the sphere, the gas inside gets hotter (Figure 2) and the pressure increases. Figure 2. The effect of temperature on gas pressure: When the hot plate is off, the pressure of the gas in the sphere is relatively low. As the gas is heated, the pressure of the gas in the sphere increases. This relationship between temperature and pressure is observed for any sample of gas confined to a constant volume. An example of experimental pressure-temperature data is shown for a sample of air under these conditions in Figure 3. We find that temperature and pressure are linearly related, and if the temperature is on the kelvin scale, then P and T are directly proportional (again, when volume and moles of gas are held constant); if the temperature on the kelvin scale increases by a certain factor, the gas pressure increases by the same factor. Figure 3. For a constant volume and amount of air, the pressure and temperature are directly proportional, provided the temperature is in kelvin. (Measurements cannot be made at lower temperatures because of the condensation of the gas.) When this line is extrapolated to lower pressures, it reaches a pressure of 0 at –273 °C, which is 0 on the kelvin scale and the lowest possible temperature, called absolute zero. Guillaume Amontons was the first to empirically establish the relationship between the pressure and the temperature of a gas (~1700), and Joseph Louis Gay-Lussac determined the relationship more precisely (~1800). Because of this, the P–T relationship for gases is known as either Amontons’s law or Gay-Lussac’s law. Under either name, it states that the pressure of a given amount of gas is directly proportional to its temperature on the kelvin scale when the volume is held constant. Mathematically, this can be written: [latex]P\propto T[/latex] [latex]P=\text{constant}\times T[/latex] [latex]P=k\times T[/latex] where ∝ means “is proportional to,” and k is a proportionality constant that depends on the identity, amount, and volume of the gas. For a confined, constant volume of gas, the ratio [latex]\frac{P}{T}[/latex] is therefore constant (i.e., [latex]\frac{P}{T}=k[/latex] ). If the gas is initially in “Condition 1” (with P = P1 and T = T1), and then changes to “Condition 2” (with P = P2 and T = T2), we have that [latex]\frac{{P}_{1}}{{T}_{1}}=k[/latex] and [latex]\frac{{P}_{2}}{{T}_{2}}=k,[/latex] which reduces to: [latex]\frac{{P}_{1}}{{T}_{1}}=\frac{{P}_{2}}{{T}_{2}}[/latex] This equation is useful for pressure-temperature calculations for a confined gas at constant volume. Note that temperatures must be on the kelvin scale for any gas law calculations (0 on the kelvin scale and the lowest possible temperature is called absolute zero). (Also note that there are at least three ways we can describe how the pressure of a gas changes as its temperature changes: We can use a table of values, a graph, or a mathematical equation.)
A can of hair spray is used until it is empty except for the propellant, isobutane gas.
Check Your LearningA sample of nitrogen, N2, occupies 45.0 mL at 27 °C and 600 torr. What pressure will it have if cooled to –73 °C while the volume remains constant? Volume and Temperature: Charles’s LawIf we fill a balloon with air and seal it, the balloon contains a specific amount of air at atmospheric pressure, let’s say 1 atm. If we put the balloon in a refrigerator, the gas inside gets cold and the balloon shrinks (although both the amount of gas and its pressure remain constant). If we make the balloon very cold, it will shrink a great deal, and it expands again when it warms up.
This video shows how cooling and heating a gas causes its volume to decrease or increase, respectively. These examples of the effect of temperature on the volume of a given amount of a confined gas at constant pressure are true in general: The volume increases as the temperature increases, and decreases as the temperature decreases. Volume-temperature data for a 1-mole sample of methane gas at 1 atm are listed and graphed in Figure 4. Figure 4. The volume and temperature are linearly related for 1 mole of methane gas at a constant pressure of 1 atm. If the temperature is in kelvin, volume and temperature are directly proportional. The line stops at 111 K because methane liquefies at this temperature; when extrapolated, it intersects the graph’s origin, representing a temperature of absolute zero. The relationship between the volume and temperature of a given amount of gas at constant pressure is known as Charles’s law in recognition of the French scientist and balloon flight pioneer Jacques Alexandre César Charles. Charles’s law states that the volume of a given amount of gas is directly proportional to its temperature on the kelvin scale when the pressure is held constant. Mathematically, this can be written as: [latex]V\propto T[/latex] [latex]V=\text{constant}\cdot T[/latex] [latex]V=k\cdot T[/latex] with k being a proportionality constant that depends on the amount and pressure of the gas. For a confined, constant pressure gas sample, [latex]\frac{V}{T}[/latex] is constant (i.e., the ratio = k), and as seen with the V–T relationship, this leads to another form of Charles’s law: [latex]\frac{{V}_{1}}{{T}_{1}}=\frac{{V}_{2}}{{T}_{2}}[/latex]
A sample of carbon dioxide, CO2, occupies 0.300 L at 10 °C and 750 torr. What volume will the gas have at 30 °C and 750 torr? Check Your LearningA sample of oxygen, O2, occupies 32.2 mL at 30 °C and 452 torr. What volume will it occupy at –70 °C and the same pressure?
Temperature is sometimes measured with a gas thermometer by observing the change in the volume of the gas as the temperature changes at constant pressure. The hydrogen in a particular hydrogen gas thermometer has a volume of 150.0 cm3 when immersed in a mixture of ice and water (0.00 °C). When immersed in boiling liquid ammonia, the volume of the hydrogen, at the same pressure, is 131.7 cm3. Find the temperature of boiling ammonia on the kelvin and Celsius scales. Check Your LearningWhat is the volume of a sample of ethane at 467 K and 1.1 atm if it occupies 405 mL at 298 K and 1.1 atm? Volume and Pressure: Boyle’s LawIf we partially fill an airtight syringe with air, the syringe contains a specific amount of air at constant temperature, say 25 °C. If we slowly push in the plunger while keeping temperature constant, the gas in the syringe is compressed into a smaller volume and its pressure increases; if we pull out the plunger, the volume increases and the pressure decreases. This example of the effect of volume on the pressure of a given amount of a confined gas is true in general. Decreasing the volume of a contained gas will increase its pressure, and increasing its volume will decrease its pressure. In fact, if the volume increases by a certain factor, the pressure decreases by the same factor, and vice versa. Volume-pressure data for an air sample at room temperature are graphed in Figure 5. Figure 5. When a gas occupies a smaller volume, it exerts a higher pressure; when it occupies a larger volume, it exerts a lower pressure (assuming the amount of gas and the temperature do not change). Since P and V are inversely proportional, a graph of 1/P vs. V is linear. Unlike the P–T and V–T relationships, pressure and volume are not directly proportional to each other. Instead, P and V exhibit inverse proportionality: Increasing the pressure results in a decrease of the volume of the gas. Mathematically this can be written: [latex]P\propto 1\text{/}V\text{ or }P=k\cdot 1\text{/}V\text{ or }P\cdot V=k\text{ or }{P}_{1}{V}_{1}={P}_{2}{V}_{2}[/latex] Figure 6. The relationship between pressure and volume is inversely proportional. (a) The graph of P vs. V is a parabola, whereas (b) the graph of (1/P) vs. V is linear. with k being a constant. Graphically, this relationship is shown by the straight line that results when plotting the inverse of the pressure [latex]\left(\frac{1}{P}\right)[/latex] versus the volume (V), or the inverse of volume [latex]\left(\frac{1}{V}\right)[/latex] versus the pressure (V). Graphs with curved lines are difficult to read accurately at low or high values of the variables, and they are more difficult to use in fitting theoretical equations and parameters to experimental data. For those reasons, scientists often try to find a way to “linearize” their data. If we plot P versus V, we obtain a hyperbola (see Figure 6). The relationship between the volume and pressure of a given amount of gas at constant temperature was first published by the English natural philosopher Robert Boyle over 300 years ago. It is summarized in the statement now known as Boyle’s law: The volume of a given amount of gas held at constant temperature is inversely proportional to the pressure under which it is measured.
The sample of gas in Figure 5 has a volume of 15.0 mL at a pressure of 13.0 psi. Determine the pressure of the gas at a volume of 7.5 mL, using:
Comment on the likely accuracy of each method. Check Your LearningThe sample of gas in Figure 5 has a volume of 30.0 mL at a pressure of 6.5 psi. Determine the volume of the gas at a pressure of 11.0 mL, using:
Comment on the likely accuracy of each method.
What do you do about 20 times per minute for your whole life, without break, and often without even being aware of it? The answer, of course, is respiration, or breathing. How does it work? It turns out that the gas laws apply here. Your lungs take in gas that your body needs (oxygen) and get rid of waste gas (carbon dioxide). Lungs are made of spongy, stretchy tissue that expands and contracts while you breathe. When you inhale, your diaphragm and intercostal muscles (the muscles between your ribs) contract, expanding your chest cavity and making your lung volume larger. The increase in volume leads to a decrease in pressure (Boyle’s law). This causes air to flow into the lungs (from high pressure to low pressure). When you exhale, the process reverses: Your diaphragm and rib muscles relax, your chest cavity contracts, and your lung volume decreases, causing the pressure to increase (Boyle’s law again), and air flows out of the lungs (from high pressure to low pressure). You then breathe in and out again, and again, repeating this Boyle’s law cycle for the rest of your life (Figure 7). Figure 7. Breathing occurs because expanding and contracting lung volume creates small pressure differences between your lungs and your surroundings, causing air to be drawn into and forced out of your lungs. Moles of Gas and Volume: Avogadro’s LawThe Italian scientist Amedeo Avogadro advanced a hypothesis in 1811 to account for the behavior of gases, stating that equal volumes of all gases, measured under the same conditions of temperature and pressure, contain the same number of molecules. Over time, this relationship was supported by many experimental observations as expressed by Avogadro’s law: For a confined gas, the volume (V) and number of moles (n) are directly proportional if the pressure and temperature both remain constant. In equation form, this is written as: [latex]\begin{array}{ccccc}V\propto n& \text{or}& V=k\times n& \text{or}& \frac{{V}_{1}}{{n}_{1}}=\frac{{V}_{2}}{{n}_{2}}\end{array}[/latex] Mathematical relationships can also be determined for the other variable pairs, such as P versus n, and n versus T. Visit this interactive PhET simulation link to investigate the relationships between pressure, volume, temperature. and amount of gas. Use the simulation to examine the effect of changing one parameter on another while holding the other parameters constant (as described in the preceding sections on the various gas laws). The Ideal Gas LawTo this point, four separate laws have been discussed that relate pressure, volume, temperature, and the number of moles of the gas:
Combining these four laws yields the ideal gas law, a relation between the pressure, volume, temperature, and number of moles of a gas: [latex]PV=nRT[/latex] where P is the pressure of a gas, V is its volume, n is the number of moles of the gas, T is its temperature on the kelvin scale, and R is a constant called the ideal gas constant or the universal gas constant. The units used to express pressure, volume, and temperature will determine the proper form of the gas constant as required by dimensional analysis, the most commonly encountered values being 0.08206 L atm mol–1 K–1 and 8.314 J L mol–1 K–1. Gases whose properties of P, V, and T are accurately described by the ideal gas law (or the other gas laws) are said to exhibit ideal behavior or to approximate the traits of an ideal gas. An ideal gas is a hypothetical construct that may be used along with kinetic molecular theory to effectively explain the gas laws as will be described in a later module of this chapter. Although all the calculations presented in this module assume ideal behavior, this assumption is only reasonable for gases under conditions of relatively low pressure and high temperature. In the final module of this chapter, a modified gas law will be introduced that accounts for the non-ideal behavior observed for many gases at relatively high pressures and low temperatures. The ideal gas equation contains five terms, the gas constant R and the variable properties P, V, n, and T. Specifying any four of these terms will permit use of the ideal gas law to calculate the fifth term as demonstrated in the following example exercises.
Methane, CH4, is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by 655 g of CH4. What is the volume of this much methane at 25 °C and 745 torr? Check Your LearningCalculate the pressure in bar of 2520 moles of hydrogen gas stored at 27 °C in the 180-L storage tank of a modern hydrogen-powered car. If the number of moles of an ideal gas are kept constant under two different sets of conditions, a useful mathematical relationship called the combined gas law is obtained: [latex]\frac{{P}_{1}{V}_{1}}{{T}_{1}}=\frac{{P}_{2}{V}_{2}}{{T}_{2}}[/latex] using units of atm, L, and K. Both sets of conditions are equal to the product of n × R (where n = the number of moles of the gas and R is the ideal gas law constant).
Figure 8. Scuba divers use compressed air to breathe while underwater. (credit: modification of work by Mark Goodchild) When filled with air, a typical scuba tank with a volume of 13.2 L has a pressure of 153 atm (Figure 8). If the water temperature is 27 °C, how many liters of air will such a tank provide to a diver’s lungs at a depth of approximately 70 feet in the ocean where the pressure is 3.13 atm? Check Your LearningA sample of ammonia is found to occupy 0.250 L under laboratory conditions of 27 °C and 0.850 atm. Find the volume of this sample at 0 °C and 1.00 atm.
Figure 9. Scuba divers, whether at the Great Barrier Reef or in the Caribbean, must be aware of buoyancy, pressure equalization, and the amount of time they spend underwater, to avoid the risks associated with pressurized gases in the body. (credit: Kyle Taylor) Whether scuba diving at the Great Barrier Reef in Australia (shown in Figure 9) or in the Caribbean, divers must understand how pressure affects a number of issues related to their comfort and safety. Pressure increases with ocean depth, and the pressure changes most rapidly as divers reach the surface. The pressure a diver experiences is the sum of all pressures above the diver (from the water and the air). Most pressure measurements are given in units of atmospheres, expressed as “atmospheres absolute” or ATA in the diving community: Every 33 feet of salt water represents 1 ATA of pressure in addition to 1 ATA of pressure from the atmosphere at sea level. As a diver descends, the increase in pressure causes the body’s air pockets in the ears and lungs to compress; on the ascent, the decrease in pressure causes these air pockets to expand, potentially rupturing eardrums or bursting the lungs. Divers must therefore undergo equalization by adding air to body airspaces on the descent by breathing normally and adding air to the mask by breathing out of the nose or adding air to the ears and sinuses by equalization techniques; the corollary is also true on ascent, divers must release air from the body to maintain equalization. Buoyancy, or the ability to control whether a diver sinks or floats, is controlled by the buoyancy compensator (BCD). If a diver is ascending, the air in his BCD expands because of lower pressure according to Boyle’s law (decreasing the pressure of gases increases the volume). The expanding air increases the buoyancy of the diver, and she or he begins to ascend. The diver must vent air from the BCD or risk an uncontrolled ascent that could rupture the lungs. In descending, the increased pressure causes the air in the BCD to compress and the diver sinks much more quickly; the diver must add air to the BCD or risk an uncontrolled descent, facing much higher pressures near the ocean floor. The pressure also impacts how long a diver can stay underwater before ascending. The deeper a diver dives, the more compressed the air that is breathed because of increased pressure: If a diver dives 33 feet, the pressure is 2 ATA and the air would be compressed to one-half of its original volume. The diver uses up available air twice as fast as at the surface. Standard Conditions of Temperature and PressureWe have seen that the volume of a given quantity of gas and the number of molecules (moles) in a given volume of gas vary with changes in pressure and temperature. Chemists sometimes make comparisons against a standard temperature and pressure (STP) for reporting properties of gases: 273.15 K and 1 atm (101.325 kPa). At STP, an ideal gas has a volume of about 22.4 L—this is referred to as the standard molar volume (Figure 10). Figure 10. Since the number of moles in a given volume of gas varies with pressure and temperature changes, chemists use standard temperature and pressure (273.15 K and 1 atm or 101.325 kPa) to report properties of gases.
The behavior of gases can be described by several laws based on experimental observations of their properties. The pressure of a given amount of gas is directly proportional to its absolute temperature, provided that the volume does not change (Amontons’s law). The volume of a given amount of gas sample is directly proportional to its absolute temperature at constant pressure (Charles’s law). The volume of a given amount of gas is inversely proportional to its pressure when temperature is held constant (Boyle’s law). Under the same conditions of temperature and pressure, equal volumes of all gases contain the same number of molecules (Avogadro’s law). The equations describing these laws are special cases of the ideal gas law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of the gas, T is its kelvin temperature, and R is the ideal (universal) gas constant. Key Equations
Glossaryabsolute zero: temperature at which the volume of a gas would be zero according to Charles’s law. Amontons’s law: (also, Gay-Lussac’s law) pressure of a given number of moles of gas is directly proportional to its kelvin temperature when the volume is held constant Avogadro’s law: volume of a gas at constant temperature and pressure is proportional to the number of gas molecules Boyle’s law: volume of a given number of moles of gas held at constant temperature is inversely proportional to the pressure under which it is measured Charles’s law: volume of a given number of moles of gas is directly proportional to its kelvin temperature when the pressure is held constant ideal gas: hypothetical gas whose physical properties are perfectly described by the gas laws ideal gas constant (R): constant derived from the ideal gas equation R = 0.08226 L atm mol–1 K–1 or 8.314 L kPa mol–1 K–1 ideal gas law: relation between the pressure, volume, amount, and temperature of a gas under conditions derived by combination of the simple gas laws standard conditions of temperature and pressure (STP): 273.15 K (0 °C) and 1 atm (101.325 kPa) standard molar volume: volume of 1 mole of gas at STP, approximately 22.4 L for gases behaving ideally |
What would be the required temperature in Celsius to change the pressure to standard pressure?
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