Q.Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

The key idea is that pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration:

$pH = -\log_{10}[H^+]$.

To find $[H^+]$, we rearrange: $[H^+] = 10^{-pH}$.

Step 1: For each fluid, substitute the given pH into $[H^+] = 10^{-pH}$.

Step 2: Compute the value using a calculator or logarithm tables.

Step 3: Express the result in scientific notation with appropriate significant figures.

• (a) Human muscle-fluid, pH 6.83: $[H^+] = 10^{-6.83} \approx 1.48 \times 10^{-7} \, \text{M}$
• (b) Human stomach fluid, pH 1.2: $[H^+] = 10^{-1.2} \approx 6.31 \times 10^{-2} \, \text{M}$
• (c) Human blood, pH 7.38: …

The pH scale is a logarithmic measure of acidity. The definition is simple but powerful:

Here $[H^+]$ is the molar concentration of hydrogen ions (in mol/L). The negative sign means that a lower pH corresponds to a higher hydrogen ion concentration — that’s why stomach acid (pH ~1.2) has far more $H^+$ than blood (pH ~7.38).

To go backwards — from pH to $[H^+]$ — we invert the logarithm. If $\text{pH} = -\log[H^+]$, then multiplying both sides by -1 gives $\log[H^+] = -\text{pH}$. Raising 10 to both sides:

That’s the only formula you need for all four parts. Each is a direct substitution.

1. Human muscle fluid, pH = 6.83

How do you evaluate $10^{-6.83}$ without a calculator in an exam? Write it as:

Now $10^{0.17}$ is the antilog of 0.17. You can recall that $\log 1.48 \approx 0.17$ (since $\log 1.5 \approx 0.176$). So $10^{0.17} \approx 1.48$.

Thus:

2. Human stomach fluid, pH = 1.2

Now $10^{0.8}$: $\log 6.31 \approx 0.8$ (since $\log 6.3 \approx 0.799$). So:

That’s about 0.063 M — a strongly acidic solution, as expected for gastric juice. …