We can use the formula for pH to calculate the concentration of hydrogen ions in each solution:
pH=−log10[H+]
For the first solution, we have:
1=−log10[H+]
Solving for [H+], we get:
[H+]=0.1 M
For the second solution, we want:
2=−log10[H+]
Solving for [H+], we get:
[H+]=0.01 M
To dilute the first solution to the desired concentration, we can use the dilution equation:
C1V1=C2V2
where C1 and V1 are the initial concentration and volume, and C2 and V2 are the final concentration and volume.
We know C1=0.1 M, C2=0.01 M, and V1=1 L. Solving for V2, we get:
V2=C2C1V1=0.01 M(0.1 M)(1 L)=10 L
Therefore, we need to add 10−1=9 liters of water to the initial solution to obtain the desired pH. Converting liters to milliliters, we get:
9 L×1 L1000 mL=9000 mL
So the volume of water needed is 9000 mL or 9,000 mL (nearest integer).
