Question

How much the hydrogen ion concentration in a solution be changed for raising the pH by 1 unit?

• A. It must be increased 10 times
• B. It must be increased by 1 mole/litre
• C. It must be decreased to $\frac{1}{10}$ th of its original value
• D. It must be decreased by 1 mole/litre

Answer 1

Answer: (C)

We know that, $pH=\log \frac{1}{[H^{+}]}$ Hence, ${(pH)}_1=-\log {[H^{+}]}_1$ ?(i) ${(pH)}_2=-\log {[H^{+}]}_2$ ?(ii) Subtract eq. (i) from equation (ii): ${(pH)}_2--{(pH)}_1=-\log {[H^{+}]}_2+\log {[H^{+}]}_1$ or $(pH)+1--{(pH)}_1=\log \frac{{[H^{+}]}_1}{{[H^{+}]}_2}$ or $1=\log {[H^{+}]}_1/{[H^{+}]}_2$ or $\frac{{[H^{+}]}_1}{{[H^{+}]}_2}=10$ $(\because 1=\log 10)$ Hence, ${[H^{+}]}_2=\frac{1}{10}{[H^{+}]}_1$ i.e. $[H^{+}]$ must be decreased $\frac{1}{10}th$ of its original volume.