Question

How many times is the $\left[ {{H}^{+}} \right]$ in the blood ($pH$=7.36) greater than in spinal fluid ($pH$=7.53)?
(A) 1 times
(B) 1.5 times
(C) 2.0 times
(D) 2.5 times

Answer 1

The comparison between two values of $pH$ is asked. Therefore, we have to take the ratio between them. Keep in mind that $pH$ is nothing but the negative logarithm of hydrogen ion concentration and $pOH$ is the negative logarithm of hydroxide ion concentration.

Complete step by step solution:
-As we know the term acid and base have been defined in different ways in chemistry. Generally, we can say that an acid is any hydrogen-containing substance which is capable of donating hydrogen ion(proton) to another substance.
-Solutions can be classified as acidic or basic on their hydrogen ion concentration relative to pure water. If the $pH$ is below seven, then the solution is acidic and if it is greater than seven the solution is said to be basic.
- The concept of $pH$can be defined as the potential hydrogen ion concentration. That is, $pH$is the negative logarithm of $\left[ {{H}^{+}} \right]$ and in a similar way $pOH$is the negative logarithm of $\left[ O{{H}^{-}} \right]$
- Since the given $pH$belongs to alkaline region, we are going to use in terms of $pOH$
We know that,
$pH+pOH=$14
$pOH$=14−$pH$
Therefore, we could find the $pOH$of both fluids from $pH$ by this relation as follows
For blood, $pOH$=14−7.36=6.64
For spinal fluid,$pOH$= 14−7.53=6.47
As we mentioned above $pOH$is the negative logarithm of $\left[ O{{H}^{-}} \right]$
$pOH$=$-{{\log }_{10}}\left[ O{{H}^{-}} \right]$
$\left[ O{{H}^{-}} \right]$= Antilog $\left[ O{{H}^{-}} \right]$
Hence by using the above relation we could find $\left[ O{{H}^{-}} \right]$for blood and spinal fluid as follows
For blood, $\left[ O{{H}^{-}} \right]$=Antilog (−6.64) = $2.29\times {{10}^{-7}}mol/d{{m}^{3}}$
For spinal fluid, $\left[ O{{H}^{-}} \right]$=Antilog (−6.47) = $3.39\times {{10}^{-7}}mol/d{{m}^{3}}$
We can use the following equation which can be derived from the concept of
$pOH$ = 14 − $pH$,
for finding the hydrogen ion concentration. That is,
$\left[ {{H}^{+}} \right]$=$\left[ O{{H}^{-}} \right]$
Hence, for finding the ratio of $\left[ {{H}^{+}} \right]$we could write as follows
$\dfrac{\left[ {{H}^{+}} \right]for\text{ }blood}{\left[ {{H}^{+}} \right]~for\text{ }spinal\text{ }fluid}=\dfrac{{{10}^{-14}}}{2.29\times {{10}^{-7}}}\times \dfrac{3.39\times {{10}^{-7}}}{{{10}^{-14}}}$ = 1.5

Therefore, the answer is option(B) 1.5 times.

Note: The answer can also be found in an easy way.
$pH$for blood =7.36
We can find the hydrogen ion concentration from $pH$as follows
$\left[ {{H}^{+}} \right]$=${{10}^{-7.36}}$M
$pH$ for spinal fluid=7.53
$\left[ {{H}^{+}} \right]$=${{10}^{-7.53}}$M
Therefore,
$\dfrac{\left[ {{H}^{+}} \right]for\text{ }blood}{\left[ {{H}^{+}} \right]~for\text{ }spinal\text{ }fluid}=\dfrac{{{10}^{-7.36}}}{{{10}^{-7.53}}}={{10}^{7.56-7.36}}={{10}^{0.17}}$ =1.5