# Question f2b83

Apr 27, 2015

The new concentration will be 1.00%.

When doing percent concentration problems, you should always start by taking a closer look at your initial solution.

A mass by volume percent concentration is expressed as grams of solute, in your case sodium chloride, per 100 mL of solution. A 1% m/v solution will have 1 g of solute in 100 mL of solution

$\text{% m/v" = "grams of solute"/"100 mL of solution} \cdot 100$

Your initial solution is 10.% m/v, which means that it has 10 g of sodium chloride in every 100 mL of solution. Since you have less than 100 mL of solution, you'll have less than 10 g of sodium chloride in your sample

"%m/v" = "x g NaCl"/"50. mL" * 100 => x = ("%m/v" * 50)/100

x = (10 * 50cancel("ml"))/(100cancel("mL")) = "5.0 g"#

This is how much sodium chloride your initial solution contains.

Now, you want to increase the volume of the solution to 500 mL. The key here is to realize that the amount of sodium chloride present will not change.

Your final solution will still have 5.0 g of $N a C l$, but its volume will be bigger. The same amount of solute in a bigger volume will automatically mean a smaller concentration.

$\text{%m/v" = "5.0 g"/"500 mL" * 100 = "1.00%}$

The volume is 10 times bigger, so the concentration must be ten times smaller.