# Question efc46

Sep 20, 2015

You need to consume $\text{4.6 L}$ of soft water to get that sodium intake.

#### Explanation:

The idea here is that you can use the percent concentration by mass of softened water to calculate how many liters would an adult need to drink in order to reach the recommended sodium intake.

A solution's percent concentration by mass is defined as the mass of the solute, in this case sodium, divided by the total mass of the solution, and multiplied by 100.

$\text{%m/m" = m_"solute"/m_"solution} \times 100$

You know that the percent concentration by mass of sodium in softened water is equal to 5.2 * 10^(-2)%, which essentiall means that you get $5.2 \cdot {10}^{- 2} \text{g}$ of sodium for every $\text{100 g}$ of softened water.

This means that you can write

2.4color(red)(cancel(color(black)("g sodium"))) * "100 g softened water"/(5.2 * 10^(-2)color(red)(cancel(color(black)("g sodium")))) = "4615.4 g softened water"

If you take soft water's density to be equal to $\text{1 g/mL}$, you can say that

4615.4color(red)(cancel(color(black)("g"))) * "1 mL"/(1color(red)(cancel(color(black)("g")))) = "4615.4 mL"

Expressed in liters and rounded to two sig figs, the answer will be

4615.4color(red)(cancel(color(black)("mL"))) * "1 L"/(1000color(red)(cancel(color(black)("mL")))) = color(green)("4.6 L")#

So, in order for an adult to consume 2.4 g of sodium, he needs to drink 4.6 L of softened water.