Questions: Determine the mass of 3.68% Na2SO4 solution that contains 0.963 g of Na+. Be sure your answer has the correct number of significant figures. g solution × 10^

Solution Steps

First, we need to find the mass of Na\(_2\)SO\(_4\) that contains 0.963 g of Na\(^+\).

The molar mass of Na\(_2\)SO\(_4\) is calculated as follows: \[ \text{Molar mass of Na}_2\text{SO}_4 = 2 \times \text{Molar mass of Na} + \text{Molar mass of S} + 4 \times \text{Molar mass of O} \] \[ = 2 \times 22.9898 + 32.065 + 4 \times 15.999 \] \[ = 45.9796 + 32.065 + 63.996 \] \[ = 142.0406 \, \text{g/mol} \]

Next, we calculate the moles of Na\(^+\) in 0.963 g: \[ \text{Moles of Na}^+ = \frac{\text{mass of Na}^+}{\text{molar mass of Na}} \] \[ = \frac{0.963 \, \text{g}}{22.9898 \, \text{g/mol}} \] \[ = 0.04188 \, \text{mol} \]

Since each mole of Na\(_2\)SO\(_4\) contains 2 moles of Na\(^+\), the moles of Na\(_2\)SO\(_4\) are: \[ \text{Moles of Na}_2\text{SO}_4 = \frac{\text{moles of Na}^+}{2} \] \[ = \frac{0.04188 \, \text{mol}}{2} \] \[ = 0.02094 \, \text{mol} \]

Now, we find the mass of Na\(_2\)SO\(_4\): \[ \text{Mass of Na}_2\text{SO}_4 = \text{moles of Na}_2\text{SO}_4 \times \text{molar mass of Na}_2\text{SO}_4 \] \[ = 0.02094 \, \text{mol} \times 142.0406 \, \text{g/mol} \] \[ = 2.973 \, \text{g} \]

Given that the solution is 3.68% Na\(_2\)SO\(_4\), we can set up the following proportion to find the total mass of the solution: \[ \frac{\text{mass of Na}_2\text{SO}_4}{\text{mass of solution}} = \frac{3.68}{100} \] \[ \frac{2.973 \, \text{g}}{\text{mass of solution}} = 0.0368 \] \[ \text{mass of solution} = \frac{2.973 \, \text{g}}{0.0368} \] \[ = 80.79 \, \text{g} \]

Final Answer