Question 10.8: Calculating pH from [H3O^+] Aspirin, which is acetylsalicyli...
Calculating pH from [ \pmb{H_{3} O^{+}} ]
Aspirin, which is acetylsalicylic acid, was the first nonsteroidal anti-inflammatory drug used to alleviate pain and fever. If a solution of aspirin has a \left[H_{3} O^{+}\right] = 1.7 \times 10^{-3} M, what is the pH of the solution?
Step \fbox{1} State the given and needed quantities.
| ANALYZE THE PROBLEM |
Given | Need | Know |
| \left[H_{3} O^{+}\right] = 1.7 \times 10^{-3} M | pH | pH = -log\left[H_{3} O^{+}\right] |
Step \fbox{2} Enter the \left[H_{3} O^{+}\right] into the pH equation.
pH = -log\left[H_{3} O^{+}\right]= -log[1.7 \times 10^{-3}]Procedure Calculator Display
Enter 1.7 and press \fbox{EE or EXP} 1.7^{00} or 1.7 00 or 1.7E00
Enter 3 and press \fbox{+/–} to change the sign. 1.7^{-03} or 1.7-03 or 1.7 E-03
Step \fbox{3} Press the log key and change the sign. Adjust the number of SFs on the right of the decimal point.
Procedure Calculator Display
\fbox{log} \fbox{+/–} 2.769551079
The steps can be combined to give the calculator sequence as follows:
pH =-log[1.7 \times 10^{-3}]=1.7 \fbox{EE or EXP} 3 \fbox{+/–} \fbox{log} \fbox{+/–}= 2.769551079
Be sure to check the instructions for your calculator. On some calculators, the log key is used first, followed by the concentration.
In a pH value, the number to the left of the decimal point is an exact number derived from the power of 10. Thus, the two SFs in the coefficient determine that there are two SFs after the decimal point in the pH value.
\overset{\text{Coefficient}}{ \underset{\text{Two SFs } }{\underset{\uparrow}{1} .\underset{\uparrow}{7} }} \times \overset{\text{Power of ten}}{ \underset{\underset{\text{Exact}}{\uparrow } }{10^{-3} M}} pH =-log[1.7 \times 10^{-3}]= \underset{\underset{\text{Exact }}{ \uparrow } }{2}.\underset{\underset{\text{Two SFs }}{ \uparrow \ \uparrow } }{77}
Guide to Calculating pH of an Aqueous Solution
Step \fbox{1}
State the given and needed quantities.
Step \fbox{2}
Enter the \left[H_{3} O^{+}\right] into the pH equation.
Step \fbox{3}
Press the log key and change the sign. Adjust the number of SFs on the right of the decimal point.