Answer :
To determine the volume of a 12 M stock solution of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] needed to make 500 mL of a 1.0 M solution, we can use the dilution equation:
[tex]\[ C_1 \times V_1 = C_2 \times V_2 \][/tex]
where:
- [tex]\( C_1 \)[/tex] is the concentration of the stock solution (12 M),
- [tex]\( V_1 \)[/tex] is the volume of the stock solution that we need to find,
- [tex]\( C_2 \)[/tex] is the concentration of the desired solution (1.0 M),
- [tex]\( V_2 \)[/tex] is the volume of the desired solution (500 mL).
Plug in the known values:
[tex]\[ 12 \, \text{M} \times V_1 = 1.0 \, \text{M} \times 500 \, \text{mL} \][/tex]
To find [tex]\( V_1 \)[/tex], solve for it by dividing both sides by 12 M:
[tex]\[ V_1 = \frac{1.0 \, \text{M} \times 500 \, \text{mL}}{12 \, \text{M}} \][/tex]
[tex]\[ V_1 = \frac{500}{12} \][/tex]
[tex]\[ V_1 = 41.67 \, \text{mL} \][/tex]
So, approximately 42 mL of the 12 M stock solution is required to make 500 mL of a 1.0 M solution of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]. Therefore, the correct answer choice is 42 mL.
[tex]\[ C_1 \times V_1 = C_2 \times V_2 \][/tex]
where:
- [tex]\( C_1 \)[/tex] is the concentration of the stock solution (12 M),
- [tex]\( V_1 \)[/tex] is the volume of the stock solution that we need to find,
- [tex]\( C_2 \)[/tex] is the concentration of the desired solution (1.0 M),
- [tex]\( V_2 \)[/tex] is the volume of the desired solution (500 mL).
Plug in the known values:
[tex]\[ 12 \, \text{M} \times V_1 = 1.0 \, \text{M} \times 500 \, \text{mL} \][/tex]
To find [tex]\( V_1 \)[/tex], solve for it by dividing both sides by 12 M:
[tex]\[ V_1 = \frac{1.0 \, \text{M} \times 500 \, \text{mL}}{12 \, \text{M}} \][/tex]
[tex]\[ V_1 = \frac{500}{12} \][/tex]
[tex]\[ V_1 = 41.67 \, \text{mL} \][/tex]
So, approximately 42 mL of the 12 M stock solution is required to make 500 mL of a 1.0 M solution of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]. Therefore, the correct answer choice is 42 mL.
