Find the percent by mass of sodium chloride in a 1.35 M NaCl solution. The density of the solution is 1.05 g/mL.

Verified step by step guidance

1. Calculate the mass of 1 liter of the NaCl solution using the density. Multiply the density of the solution (1.05 g/mL) by the volume of the solution (1000 mL for 1 liter).
2. Determine the mass of NaCl in one liter of the solution. Use the molarity of the solution (1.35 M), which means there are 1.35 moles of NaCl per liter. Convert moles of NaCl to grams using the molar mass of NaCl (58.44 g/mol).
3. Calculate the percent by mass of NaCl in the solution. Use the formula: \(\text{Percent by mass} = \left(\frac{\text{mass of NaCl}}{\text{mass of solution}}\right) \times 100\%\).
4. Substitute the values obtained from steps 1 and 2 into the formula from step 3.
5. Simplify the expression to find the percent by mass of NaCl in the solution.

Key Concepts

Molarity (M)

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. In this case, a 1.35 M NaCl solution means there are 1.35 moles of sodium chloride dissolved in one liter of the solution. Understanding molarity is essential for calculating the mass of solute in a given volume of solution.

Density

Density is the mass of a substance per unit volume, typically expressed in grams per milliliter (g/mL) for liquids. The density of the NaCl solution is given as 1.05 g/mL, which allows us to convert the volume of the solution into mass. This conversion is crucial for determining the total mass of the solution needed to find the percent by mass of sodium chloride.

Percent by Mass

Percent by mass is a way to express the concentration of a component in a mixture, calculated as the mass of the solute divided by the total mass of the solution, multiplied by 100. To find the percent by mass of sodium chloride in the solution, we need to determine the mass of NaCl and the total mass of the solution, then apply this formula. This concept is fundamental for understanding the composition of solutions.