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Chapter 4: Problem 31

Calculate the molarity of each of these solutions. a. \(A 5.623-g\) sample of \({NaHCO}_{3}\) is dissolved in enough water to make 250.0 \({mL}\) of solution. b. A \(184.6-{mg}\) sample of \({K}_{2} {Cr}_{2} {O}_{7}\) is dissolved in enough water to make 500.0 \({mL}\) of solution. c. A 0.1025 -g sample of copper metal is dissolved in 35 \({mL}\) of concentrated \({HNO}_{3}\) to form \({Cu}^{2+}\) ions and then water is added to make a total volume of 200.0 \({mL}\) . (Calculate the molarity of ${Cu}^{2+} . )$

Short Answer

Expert verified
The molarity of the solutions are as follows: a. The molarity of the \(NaHCO_3\) solution is \(0.268\) mol/L. b. The molarity of the \(K_2Cr_2O_7\) solution is \(0.001256\) mol/L. c. The molarity of the \(Cu^{2+}\) solution is \(0.008065\) mol/L.

Step by step solution

01

Calculating the moles of \(NaHCO_3\)

First, calculate the molar mass of \(NaHCO_3\): Na=22.99 g/mol, H=1.01 g/mol, C=12.01 g/mol, and O=16.00 g/mol, so the molar mass of \(NaHCO_3\) = 22.99 + 1.01 + 12.01 + 3*16.00 = 84.01 g/mol. Now, divide the given mass of \(NaHCO_3\) (5.623 g) by its molar mass (84.01 g/mol) to find the moles of solute: moles = 5.623 g / 84.01 g/mol ≈ 0.067 mole.
02

Convert the volume of the solution to liters

The volume of the solution is given as 250.0 mL. Convert this to liters by dividing by 1000 mL/L: 250.0 mL * (1 L / 1000 mL) = 0.250 L.
03

Calculate the molarity

Now, divide the moles of solute by the volume of the solution (in liters) to find the molarity: molarity = \(0.067\) moles / \(0.250\) L ≈ 0.268 mol/L. The molarity of the \(NaHCO_3\) solution is \(0.268\) mol/L. #b. Calculate the molarity of the \(K_2Cr_2O_7\) solution.#
04

Calculating the moles of \(K_2Cr_2O_7\)

Calculate the molar mass of \(K_2Cr_2O_7\): K=39.10 g/mol, Cr=51.99 g/mol, and O=16.00 g/mol, so the molar mass of \(K_2Cr_2O_7\) = 2*39.10 + 2*51.99 + 7*16.00 = 294.18 g/mol. Convert the given mass of \(K_2Cr_2O_7\) (184.6 mg) to grams by dividing by 1000 mg/g: 184.6 mg * (1 g / 1000 mg) = 0.1846 g. Now, divide the mass of \(K_2Cr_2O_7\) (0.1846 g) by its molar mass (294.18 g/mol) to find the moles of solute: moles = 0.1846 g / 294.18 g/mol ≈ 0.000628 mole.
05

Convert the volume of the solution to liters

The volume of the solution is given as 500.0 mL. Convert this to liters by dividing by 1000 mL/L: 500.0 mL * (1 L / 1000 mL) = 0.500 L.
06

Calculate the molarity

Now, divide the moles of solute by the volume of the solution (in liters) to find the molarity: molarity = \(0.000628\) moles / \(0.500\) L ≈ 0.001256 mol/L. The molarity of the \(K_2Cr_2O_7\) solution is \(0.001256\) mol/L. #c. Calculate the molarity of the \(Cu^{2+}\) solution.#
07

Calculating the moles of \(Cu\)

Calculate the molar mass of \(Cu\): Cu=63.55 g/mol. Now, divide the given mass of \(Cu\) (0.1025 g) by its molar mass (63.55 g/mol) to find the moles of solute: moles = 0.1025 g / 63.55 g/mol ≈ 0.001613 mole.
08

Convert the volume of the solution to liters

The final volume of the solution is given as 200.0 mL. Convert this to liters by dividing by 1000 mL/L: 200.0 mL * (1 L / 1000 mL) = 0.200 L.
09

Calculate the molarity of the \(Cu^{2+}\) ions

Now, divide the moles of \(Cu^{2+}\) ions by the volume of the solution (in liters) to find the molarity: molarity = \(0.001613\) moles / \(0.200\) L ≈ 0.008065 mol/L. The molarity of the \(Cu^{2+}\) solution is \(0.008065\) mol/L.

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