# A stock solution contains 5 g per 100 ml of sucrose. How many ml of this stock solution would you use to prepare 1 litre of sucrose solution at a concentration of 0.25 g per litre?

Aug 13, 2018

5 mL

#### Explanation:

It's a dilution problem since it starts with a concentrated stock solution and a lower concentration solution is prepared from it.

First of all, we'll need to do is calculate the 2 concentrations that are given:

We can do that using 2 ways:

• $M o l a r i t y = \text{mol" / "volume in L}$
Using this formula will require additional calculation, converting from grams to mol using molar mass of sucrose.

• %(m/v)=("g of solute")/("mL of solution")xx 100%
I'll proceed using this concentration. Take note on the unit required for mass (g) and volume (mL).

"Concentration of stock solution" =C_1 = ("5g")/(100 mL)xx100%=5%

"Concentration of diluted solution" =C_2 = ("0.25g")/(1000 mL)xx100%=0.025%

We also know from the question, that the final volume of solution ${V}_{2}$) is 1 L = 1000 mL.

Since we need to find out the volume of stock solution used (${V}_{1}$) to prepare the diluted solution, we'll use the dilution formula:

${C}_{1} {V}_{1} = {C}_{2} {V}_{2}$

5% xx V_1 = 0.025% xx 1000 mL

${V}_{1} = \frac{0.025 \times 1000}{5} = \text{5 mL}$