GED Science - Making Solutions

A student is asked to make $\small 4L$ of $\small 0.125M$ NaCl solution. The student is given a stock solution of $\small 5M$ NaCl. What volumes of stock NaCl solution and pure water could be used to make the desired final solution?

$100 mL\ \text{stock NaCl and}\ 3900mL\ \text{water}$

$100 mL\ \text{stock NaCl and}\ 4000mL\ \text{water}$

$125 mL\ \text{stock NaCl and}\ 3875mL\ \text{water}$

$125 mL\ \text{stock NaCl and}\ 4000mL\ \text{water}$

Explanation

Convert liters to mL:

$\small \frac{4L}{1}=\frac{1000mL}{1L}=4000 mL$

This is the TOTAL volume of the solution. Next, determine how much NaCl to add.

$\small c_1v_1=c_2v_2$

$\small c_1=5.0M$

$\small c_2=0.125M$

$\small v_2=4000mL$

$\small (5.0M)v_1=(0.125M)(4000mL)$

$\small (5.0M)v_1=500MmL$

$\small \frac{(5.0M)v_1}{5.0M}=\frac{500MmL}{5.0M}$

$\small v_1=100mL$

Therefore, $\small 100mL$ of stock NaCl must be added. Subtract this volume from $\small 4000 mL$ to determine the amount of water used in the final solution.

$\small 4000mL-100mL=3900mL\ water$

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