Question

how many grams of salt are needed to make 645 g of salt water that is 31.5% salt by mass? mass of salt:

Explanation:

Step1: Identify the formula

The mass - percentage formula is $\text{Mass}\%=\frac{\text{Mass of solute}}{\text{Mass of solution}}\times100\%$. We want to find the mass of the solute (salt), and we know the mass of the solution ($m_{solution} = 645\ g$) and the mass - percentage ($\text{Mass}\%=31.5\%$). Rearranging the formula for the mass of the solute gives $m_{solute}=\frac{\text{Mass}\%}{100\%}\times m_{solution}$.

Step2: Substitute the values

Substitute $\text{Mass}\% = 31.5\%$ and $m_{solution}=645\ g$ into the formula: $m_{solute}=\frac{31.5}{100}\times645$.
$m_{solute}=0.315\times645 = 203.175\ g$.

Answer:

$203.175\ g$