Acids and Bases - MCAT Chemical and Physical Foundations of Biological Systems

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Question

What is the resulting pH when 7.0g of HCl is dissolved in 3L of water?

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Answer

HCl is a strong acid; it will fully dissociate in water, meaning that the concentration of H+ is equal to the concentration of HCl (they are in a 1 : 1 ratio). 7.0g of HCl is equal to 0.2mol (MW of HCl is 35.3g/mol). 0.2mol HCl goes into 3L of water, resulting in a concentration of 0.067M, or 6.7times 10^{-2}.

Now we know that \dpi{100} \small \left [ H^{+} \right ]=6.7\times 10^{-2} and pH=-log\[H+\]. Using our trick for -log, we can see that \dpi{100} \small 1\times 10^{-1}> 6.7\times 10^{-2}> 1\times 10^{-2}. Since -logleft (1times 10^{-1} right )=1 and -logleft (1times 10^{-2} right )=2, we know our answer is between 1 and 2.

6.7times 10^{-2} is closer to 1times 10^{-1}, so we can pick the answer closer to 1. i.e. 1.2.

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