You want to add some sections to the porch seen above. Before you go to the hardware store to buy lumber, you need to determine the unit composition (the material between two large uprights). You count how many posts, how many boards, how many rails – then you decide how many sections you want to add before you calculate the amount of building material needed for your porch expansion.
Stoichiometry problems can be characterized by two things: (1) the information given in the problem, and (2) the information that is to be solved for, referred to as the unknown. The given and the unknown may both be reactants, both be products, or one may be a reactant while the other is a product. The amounts of the substances can be expressed in moles. However, in a laboratory situation, it is common to determine the amount of a substance by finding its mass in grams. The amount of a gaseous substance may be expressed by its volume. In this concept, we will focus on the type of problem where both the given and the unknown quantities are expressed in moles.  Chemical equations express the amounts of reactants and products in a reaction. The coefficients of a balanced equation can represent either the number of molecules or the number of moles of each substance. The production of ammonia \(\left( \ce{NH_3} \right)\) from nitrogen and hydrogen gases is an important industrial reaction called the Haber process, after German chemist Fritz Haber. \[\ce{N_2} \left( g \right) + 3 \ce{H_2} \left( g \right) \rightarrow 2 \ce{NH_3} \left( g \right)\nonumber \] The balanced equation can be analyzed in several ways, as shown in the figure below. We see that 1 molecule of nitrogen reacts with 3 molecules of hydrogen to form 2 molecules of ammonia. This is the smallest possible relative amount of the reactants and products. To consider larger relative amounts, each coefficient can be multiplied by the same number. For example, 10 molecules of nitrogen would react with 30 molecules of hydrogen to produce 20 molecules of ammonia. The most useful quantity for counting particles is the mole. So if each coefficient is multiplied by a mole, the balanced chemical equation tells us that 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia. This is the conventional way to interpret any balanced chemical equation. Finally, if each mole quantity is converted to grams by using the molar mass, we can see that the law of conservation of mass is followed. \(1 \: \ce{mol}\) of nitrogen has a mass of \(28.02 \: \text{g}\), while \(3 \: \text{mol}\) of hydrogen has a mass of \(6.06 \: \text{g}\), and \(2 \: \text{mol}\) of ammonia has a mass of \(34.08 \: \text{g}\). \[28.02 \: \text{g} \: \ce{N_2} + 6.06 \: \text{g} \: \ce{H_2} \rightarrow 34.08 \: \text{g} \: \ce{NH_3}\nonumber \] Mass and the number of atoms must be conserved in any chemical reaction. The number of molecules is not necessarily conserved. A mole ratio is a conversion factor that relates the amounts in moles of any two substances in a chemical reaction. The numbers in a conversion factor come from the coefficients of the balanced chemical equation. The following six mole ratios can be written for the ammonia forming reaction above. \[\begin{array}{ccc} \dfrac{1 \: \text{mol} \: \ce{N_2}}{3 \: \text{mol} \: \ce{H_2}} & or & \dfrac{3 \: \text{mol} \: \ce{H_2}}{1 \: \text{mol} \: \ce{N_2}} \\ \dfrac{1 \: \text{mol} \: \ce{N_2}}{2 \: \text{mol} \: \ce{NH_3}} & or & \dfrac{2 \: \text{mol} \: \ce{NH_3}}{1 \: \text{mol} \: \ce{N_2}} \\ \dfrac{3 \: \text{mol} \: \ce{H_2}}{2 \: \text{mol} \: \ce{NH_3}} & or & \dfrac{2 \: \text{mol} \: \ce{NH_3}}{3 \: \text{mol} \: \ce{H_2}} \end{array}\nonumber \] In a mole ratio problem, the given substance, expressed in moles, is written first. The appropriate conversion factor is chosen in order to convert from moles of the given substance to moles of the unknown.
Example \(\PageIndex{1}\): Mole Ratio How many moles of ammonia are produced if 4.20 moles of hydrogen are reacted with an excess of nitrogen? Solution Step 1: List the known quantities and plan the problem. Known Unknown The conversion is from \(\text{mol} \: \ce{H_2}\) to \(\text{mol} \: \ce{NH_3}\). The problem states that there is an excess of nitrogen, so we do not need to be concerned with any mole ratio involving \(\ce{N_2}\). Choose the conversion factor that has the \(\ce{NH_3}\) in the numerator and the \(\ce{H_2}\) in the denominator. Step 2: Solve. \[4.20 \: \text{mol} \: \ce{H_2} \times \dfrac{2 \: \text{mol} \: \ce{NH_3}}{3 \: \text{mol} \: \ce{H_2}} = 2.80 \: \text{mol} \: \ce{NH_3}\nonumber \] The reaction of \(4.20 \: \text{mol}\) of hydrogen with excess nitrogen produces \(2.80 \: \text{mol}\) of ammonia. Step 3: Think about your result. The result corresponds to the 3:2 ratio of hydrogen to ammonia from the balanced equation.
Updated December 15, 2020 By Chris Deziel
When analyzing solutions, chemists measure concentrations of components in moles. The mole fraction of a solute is the ratio of the number of moles of that solute to the total number of moles of solute and solvent in solution. Because it's a ratio of moles to moles, the mole fraction is a dimensionless number, and of course, it's always less than one.
The mole fraction formula is straightforward. In any solution, the mole fraction of solute A is: \text{mole fraction of A} = \frac{\text{moles of A}}{\text{total moles}}
and the mole fraction of the solvent: \text{mole fraction of solvent} = \frac{\text{moles of solvent}}{\text{total moles}}
In some situations, you may not be given the number of moles directly. You can calculate it if you know the chemical formulas of the compounds and their weights or volumes. To do this, it helps to know what a mole is.
The mole fraction formula for a solution with containing one or more solutes is: Mole fraction of each solute = Number of moles of that solute divided by the total number of moles of all solutes and the solvent.
Each element in the periodic table has a characteristic mass, and by virtue of this, every compound also has a characteristic mass. At the atomic level, mass is measured in atomic mass units, but chemists need a way to express mass in macroscopic terms. To this end, they define a mole of any element or compounds as Avogadro's number (6.022 × 1023) of atoms or molecules. The mass of this many particles, measured in grams, is the same number as the molecular mass, measured in atomic mass units.
The definition of a mole is thus the mass of any compound, measured in grams, that equals the masses of the component elements measured in atomic mass units. To calculate the number of moles of a compound you have on hand, you divide the mass by the mass of one mole of the compound, which you can calculate from the periodic table.
The mole fraction formula is particularly easy to understand and use if you happen to know the number of moles of all of the solutes and the solvent. For example, suppose you have 2 moles of carbon tetrachloride (CCl4), 3 moles of benzene (C6H6) and 4 moles of acetone (C3H6O). The total number of moles in solution is 9. The mole fraction equation tells you that the mole fraction of carbon tetrachloride is 2/9 = 0.22. Similarly, the mole fraction of benzene is 3/9 = 0.33 and the mole fraction of acetone is 4/9 = 0.44.
Things get more complicated if you only know the mass of one or more components of a solution, but only a little more. All you have to do is convert the mass of the component to number of moles, and that's a straightforward arithmetic problem, as long as you know the chemical formula.
Suppose you dissolve 77 grams of carbon tetrachloride (CCl4) in 78 grams of acetone (C3H6O). What are the mole fractions of each compound in the solution?
Resist the urge to divide the mass of carbon tetrachloride by that of acetone. Since they are almost the same, the result would be 0.5 for each compound, and that would give an incorrect result for acetone. First, you have to convert the masses to the number of moles of each compound, and to do that, you have to look up the atomic masses of each of the elements in the periodic table.
The atomic mass of carbon is 12.0 amu (rounding to one decimal place) and that of chlorine is 35.5 amu, so one mole of carbon tetrachloride weighs 154 grams. You have 77 grams, which is 77/154 = 0.5 moles.
Noting that the atomic mass of hydrogen is 1 amu and that of oxygen is 16 amu, the molar mass of acetone is 58 grams. You have 78 grams, which is 1.34 moles. That means the total number of moles in solution is 1.84. Now you're ready to calculate mole fractions using the mole fraction equation. \text{mole fraction of carbon tetrachloride}=\frac{0.5\text{ moles}}{1.84\text{ moles}}=0.27\\\text{ }\\\text{ mole fraction of acetone}=\frac{1.34\text{ moles}}{1.84\text{ moles}}=0.73 |
What is the ratio of the number of moles of one component of a mixture to the total number of moles of all components?
Postagens relacionadas
direito autoral © 2024 aprendervalor Inc.
