What is the number of moles in 3.0 Litres of 3m NaCl?

In Example 3, you calculated that the concentration of a solution containing 90.00 g of ammonium dichromate in a final volume of 250 mL is 1.43 M. Let’s consider in more detail exactly what that means. Ammonium dichromate is an ionic compound that contains two NH4+ ions and one Cr2O72− ion per formula unit. Like other ionic compounds, it is a strong electrolyte that dissociates in aqueous solution to give hydrated NH4+ and Cr2O72− ions:

Figure 4.9 Dissolution of 1 mol of an Ionic Compound

In this case, dissolving 1 mol of (NH4)2Cr2O7 produces a solution that contains 1 mol of Cr2O72− ions and 2 mol of NH4+ ions. (Water molecules are omitted from a molecular view of the solution for clarity.)

When we carry out a chemical reaction using a solution of a salt such as ammonium dichromate, we need to know the concentration of each ion present in the solution. If a solution contains 1.43 M (NH4)2Cr2O7, then the concentration of Cr2O72− must also be 1.43 M because there is one Cr2O72− ion per formula unit. However, there are two NH4+ ions per formula unit, so the concentration of NH4+ ions is 2 × 1.43 M = 2.86 M. Because each formula unit of (NH4)2Cr2O7 produces three ions when dissolved in water (2NH4+ + 1Cr2O72−), the total concentration of ions in the solution is 3 × 1.43 M = 4.29 M.

What are the concentrations of all species derived from the solutes in these aqueous solutions?

1. 0.21 M NaOH
2. 3.7 M (CH3)CHOH
3. 0.032 M In(NO3)3

Given: molarity

Asked for: concentrations

Strategy:

A Classify each compound as either a strong electrolyte or a nonelectrolyte.

B If the compound is a nonelectrolyte, its concentration is the same as the molarity of the solution. If the compound is a strong electrolyte, determine the number of each ion contained in one formula unit. Find the concentration of each species by multiplying the number of each ion by the molarity of the solution.

Solution:

1. Sodium hydroxide is an ionic compound that is a strong electrolyte (and a strong base) in aqueous solution:

   NaOH(s) → H 2 O(l) Na + (aq) + OH – (aq)

   B Because each formula unit of NaOH produces one Na+ ion and one OH− ion, the concentration of each ion is the same as the concentration of NaOH: [Na+] = 0.21 M and [OH−] = 0.21 M.

2. A The formula (CH3)2CHOH represents 2-propanol (isopropyl alcohol) and contains the –OH group, so it is an alcohol. Recall from Section 4.1 "Aqueous Solutions" that alcohols are covalent compounds that dissolve in water to give solutions of neutral molecules. Thus alcohols are nonelectrolytes.

   B The only solute species in solution is therefore (CH3)2CHOH molecules, so [(CH3)2CHOH] = 3.7 M.

3. A Indium nitrate is an ionic compound that contains In3+ ions and NO3− ions, so we expect it to behave like a strong electrolyte in aqueous solution:

   In(NO 3 ) 3 (s) → H 2 O(l) In 3+ (aq) + 3NO 3 – (aq)

   B One formula unit of In(NO3)3 produces one In3+ ion and three NO3− ions, so a 0.032 M In(NO3)3 solution contains 0.032 M In3+ and 3 × 0.032 M = 0.096 M NO3–—that is, [In3+] = 0.032 M and [NO3−] = 0.096 M.

Exercise

What are the concentrations of all species derived from the solutes in these aqueous solutions?

1. 0.0012 M Ba(OH)2
2. 0.17 M Na2SO4
3. 0.50 M (CH3)2CO, commonly known as acetone

Answer:

1. [Ba2+] = 0.0012 M; [OH−] = 0.0024 M
2. [Na+] = 0.34 M; [SO42−] = 0.17 M
3. [(CH3)2CO] = 0.50 M

The concentration of a substance is the quantity of solute present in a given quantity of solution. Concentrations are usually expressed as molarity, the number of moles of solute in 1 L of solution. Solutions of known concentration can be prepared either by dissolving a known mass of solute in a solvent and diluting to a desired final volume or by diluting the appropriate volume of a more concentrated solution (a stock solution) to the desired final volume.

1. Which of the representations best corresponds to a 1 M aqueous solution of each compound? Justify your answers.

   1. NH3
   2. HF
   3. CH3CH2CH2OH

   4. Na2SO4

2. Which of the representations shown in Problem 1 best corresponds to a 1 M aqueous solution of each compound? Justify your answers.

   1. CH3CO2H
   2. NaCl
   3. Na2S
   4. Na3PO4
   5. acetaldehyde

3. Would you expect a 1.0 M solution of CaCl2 to be a better conductor of electricity than a 1.0 M solution of NaCl? Why or why not?

4. An alternative way to define the concentration of a solution is molality, abbreviated m. Molality is defined as the number of moles of solute in 1 kg of solvent. How is this different from molarity? Would you expect a 1 M solution of sucrose to be more or less concentrated than a 1 m solution of sucrose? Explain your answer.

5. What are the advantages of using solutions for quantitative calculations?

5. If the amount of a substance required for a reaction is too small to be weighed accurately, the use of a solution of the substance, in which the solute is dispersed in a much larger mass of solvent, allows chemists to measure the quantity of the substance more accurately.

1. Calculate the number of grams of solute in 1.000 L of each solution.

   1. 0.2593 M NaBrO3
   2. 1.592 M KNO3
   3. 1.559 M acetic acid
   4. 0.943 M potassium iodate

2. Calculate the number of grams of solute in 1.000 L of each solution.

   1. 0.1065 M BaI2
   2. 1.135 M Na2SO4
   3. 1.428 M NH4Br
   4. 0.889 M sodium acetate

3. If all solutions contain the same solute, which solution contains the greater mass of solute?

   1. 1.40 L of a 0.334 M solution or 1.10 L of a 0.420 M solution
   2. 25.0 mL of a 0.134 M solution or 10.0 mL of a 0.295 M solution
   3. 250 mL of a 0.489 M solution or 150 mL of a 0.769 M solution

4. Complete the following table for 500 mL of solution.

5. What is the concentration of each species present in the following aqueous solutions?

   1. 0.489 mol of NiSO4 in 600 mL of solution
   2. 1.045 mol of magnesium bromide in 500 mL of solution
   3. 0.146 mol of glucose in 800 mL of solution
   4. 0.479 mol of CeCl3 in 700 mL of solution

6. What is the concentration of each species present in the following aqueous solutions?

   1. 0.324 mol of K2MoO4 in 250 mL of solution
   2. 0.528 mol of potassium formate in 300 mL of solution
   3. 0.477 mol of KClO3 in 900 mL of solution
   4. 0.378 mol of potassium iodide in 750 mL of solution

7. What is the molar concentration of each solution?

   1. 8.7 g of calcium bromide in 250 mL of solution
   2. 9.8 g of lithium sulfate in 300 mL of solution
   3. 12.4 g of sucrose (C12H22O11) in 750 mL of solution
   4. 14.2 g of iron(III) nitrate hexahydrate in 300 mL of solution

8. What is the molar concentration of each solution?

   1. 12.8 g of sodium hydrogen sulfate in 400 mL of solution
   2. 7.5 g of potassium hydrogen phosphate in 250 mL of solution
   3. 11.4 g of barium chloride in 350 mL of solution
   4. 4.3 g of tartaric acid (C4H6O6) in 250 mL of solution

9. Give the concentration of each reactant in the following equations, assuming 20.0 g of each and a solution volume of 250 mL for each reactant.

   1. BaCl2(aq) + Na2SO4(aq) →
   2. Ca(OH)2(aq) + H3PO4(aq) →
   3. Al(NO3)3(aq) + H2SO4(aq) →
   4. Pb(NO3)2(aq) + CuSO4(aq) →
   5. Al(CH3CO2)3(aq) + NaOH(aq) →

10. An experiment required 200.0 mL of a 0.330 M solution of Na2CrO4. A stock solution of Na2CrO4 containing 20.0% solute by mass with a density of 1.19 g/cm3 was used to prepare this solution. Describe how to prepare 200.0 mL of a 0.330 M solution of Na2CrO4 using the stock solution.

11. Calcium hypochlorite [Ca(OCl)2] is an effective disinfectant for clothing and bedding. If a solution has a Ca(OCl)2 concentration of 3.4 g per 100 mL of solution, what is the molarity of hypochlorite?

12. Phenol (C6H5OH) is often used as an antiseptic in mouthwashes and throat lozenges. If a mouthwash has a phenol concentration of 1.5 g per 100 mL of solution, what is the molarity of phenol?

13. If a tablet containing 100 mg of caffeine (C8H10N4O2) is dissolved in water to give 10.0 oz of solution, what is the molar concentration of caffeine in the solution?

14. A certain drug label carries instructions to add 10.0 mL of sterile water, stating that each milliliter of the resulting solution will contain 0.500 g of medication. If a patient has a prescribed dose of 900.0 mg, how many milliliters of the solution should be administered?