What is the percent by mass of a solution that is prepared by mixing 3.785 grams of sodium chloride with 43.7 milliliters of water (assume the density of water is 1.00 g/mL)? Thanks!?

Jul 7, 2015

The solution is 7.97% m/m.

Explanation:

In order to determine a solution's percent concentration by mass, you need to know the mass of the solute, in your case sodium chloride, and the mass of the entire solution, which contains sodium chloride and water.

Since you know what the density of water is, you can use its volume to determine its mass.

$\rho = \frac{m}{V} \implies m = \rho \cdot V$

43.7cancel("mL") * "1.00 g"/(1cancel("mL")) = "43.7 g"

This means that the mass of the solution will be

${m}_{\text{solution" = m_"sodium chloride" + m_"water}}$

${m}_{\text{solution" = 3.785 + 43.7 = "47.485 g}}$

Therefore, your solution's percent concentration by mass will be

$\text{%m/m" = m_"sodium chloride"/m_"solution} \cdot 100$

"%m/m" = (3.785cancel("g"))/(47.485cancel("g")) * 100 = color(green)("7.97%")

Your sodium chloride solution is 7.97% m/m.