Question

What is the molarity of \(\mathrm{Na}^{+}\) in a solution of \(\mathrm{NaCl}\) whose salinity is \(5.6\) if the solution has a density of \(1.03 \mathrm{~g} / \mathrm{mL}\) ?

Short answer

The molarity of Na+ ions in the solution can be calculated using the following steps: 1. Mass of the solution: \(m_{solution} = 1.03\ \text{g/mL} \times 1000\ \text{mL} = 1030\ \text{g}\) 2. Mass of NaCl in the solution: \(m_{NaCl} = 1030\ \text{g} \times \frac{5.6}{100} = 57.68\ \text{g}\) 3. Moles of NaCl: \(n_{NaCl} = \frac{57.68\ \text{g}}{58.44\ \text{g/mol}} = 0.987\ \text{mol}\) 4. Moles of Na+: \(n_{Na^{+}} = n_{NaCl} = 0.987\ \text{mol}\) 5. Molarity of Na+: \(M_{Na^{+}} = \frac{0.987\ \text{mol}}{1\ \text{L}} = 0.987\ \text{M}\) Therefore, the molarity of Na+ ions in the solution is \(0.987\ \text{M}\).

Step-by-step solution

Calculate the mass of the solution

To compute the mass of the solution, we need to determine its volume first. Assuming 1 L of the solution, the mass of the solution will be the density multiplied by the volume. Let the mass of the solution be denoted by the variable '\(m_{solution}\)': \[ m_{solution} = density \times volume \] \[ m_{solution} = 1.03\ \text{g/mL} \times 1000\ \text{mL} \]

Calculate the mass of NaCl in the solution

Now that we have the mass of the solution, we can calculate the mass of NaCl in the solution. Using the salinity (\(5.6\%\)), we can find the mass of NaCl by multiplying the mass of the solution by the salinity (converted to a decimal by dividing by 100). Let the mass of NaCl be denoted by the variable '\(m_{NaCl}\)': \[ m_{NaCl} = m_{solution} \times \frac{salinity}{100} \]

Calculate the moles of NaCl

In order to determine the moles of NaCl, divide the mass of NaCl by its molar mass (\(22.99 \ \text{g/mol } + 35.45 \ \text{g/mol} = 58.44 \ \text{g/mol}\)). Let the moles of NaCl be denoted by the variable '\(n_{NaCl}\)': \[ n_{NaCl} = \frac{m_{NaCl}}{58.44\ \text{g/mol}} \]

Calculate the moles of Na+ ions

Since there is one Na+ ion for every molecule of NaCl, the moles of Na+ ions will be equal to the moles of NaCl: \[ n_{Na^{+}} = n_{NaCl} \]

Calculate the molarity of Na+ ions

Finally, to find the molarity of Na+ ions in the solution, divide the moles of Na+ ions by the volume of the solution (in liters). Let the molarity of Na+ ions be denoted by the variable '\(M_{Na^{+}}\)': \[ M_{Na^{+}} = \frac{n_{Na^{+}}}{1\ \text{L}} \] Now, you can plug in the values and calculate \(M_{Na^{+}}\).