Question

How many times is the $\left[H^{+}\right]$ in the blood ($pH=7.36$) greater than in spinal fluid ($pH=7.53$)?

• A. $1.0$ times
• B. $1.5$ times
• C. $2.0$ times
• D. $2.5$ times

Answer 1

Answer: (B)

$1.5$ times

Note: Since the comparison between two values of $pH$ is asked, we have to take their ratio. But, since both the fluids are alkaline (basic as $pH>7$), hence, we need to solve this question in terms of $pOH$ and not $pH$.
We know that,
$pH+pOH=14$
$pOH=14-pH$
For Blood, $pOH=14-7.36=6.64$
For Spinal Fluid, $pOH=14-7.53=6.47$
Also,
$pOH=-lo{g}_{10}\left[O{H}^{-}\right]$
$\left[O{H}^{-}\right]={10}^{-pOH}$ or $Antilog(-pOH)$
Hence, using the above relation,
For Blood, $\left[O{H}^{-}\right]$=$Antilog(-6.64)=2.29\times {10}^{-7}mol/d{m}^3$
For Spinal Fluid, $\left[O{H}^{-}\right]$=$Antilog(-6.47)=3.39\times {10}^{-7}mol/d{m}^3$
For getting $\left[H^{+}\right]$, we use,
$\left[H^{+}\right]={10}^{-14}/\left[O{H}^{-}\right]$
which is mentioned in the concept attached.
Hence,
$\frac{\left[H^{+}\right]forBlood}{\left[H^{+}\right]foSpinalFluid}=\frac{{10}^{-14}}{2.29\times {10}^{-7}}\times \frac{3.39\times {10}^{-7}}{{10}^{-14}}=1.48$