Calculating Water pH at 40°C
The ionic product of water ($K_w$) changes with temperature. At 40°C, the given $K_w$ is $2.92 \times 10^{-14}$ $M^2$. We can calculate the pH using this value.
pH Calculation Steps
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Relationship in Pure Water: In pure water, the concentration of hydrogen ions ($[H^+]$) equals the concentration of hydroxide ions ($[OH^-]$). Therefore, $K_w = [H^+] \times [OH^-] = [H^+]^2$.
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Calculate Hydrogen Ion Concentration ($[H^+]$): Take the square root of $K_w$ to find $[H^+]$. $[H^+] = \sqrt{K_w}$ $[H^+] = \sqrt{2.92 \times 10^{-14} \text{ M}^2}$ $[H^+] \approx 1.7088 \times 10^{-7} \text{ M}$
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Calculate pH: Use the formula $pH = -\log_{10}[H^+]$. $pH = -\log_{10}(1.7088 \times 10^{-7})$ $pH \approx -(-6.7673)$ $pH \approx 6.7673$
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Rounding Off: Round the calculated pH to 2 decimal places as required. $pH \approx 6.77$
The calculated pH of water at 40°C is approximately 6.77, which falls within the range of 6.76 to 6.78.
Important Questions from Chemical Biology {p}K_a Henderson Hasselbalch
- The equilibrium dissociation constant of acetic acid is $1.74 \times 10^{-5}$ $M$. The $pK_a$ of acetic acid (rounded off to one decimal place) is ________.
- In a lactic acid solution at pH $4.8$, the concentrations of lactic acid and lactate are $0.01$ M and $0.087$ M, respectively. The calculated pKa of lactic acid is ________ (Round off to one decimal place)
An aqueous solution of aspirin (HA) is prepared at pH 7.4. The ratio of concentration of $A^-$ and HA at equilibrium is ________ (round off to the nearest integer).
Given: $K_a$ of aspirin is $3.98 \times 10^{-4}$
- If 50 mL of 0.02 M HCl is added to 950 mL of $H_2O$, then the pH of the final solution will be _________
One litre of phosphate buffer was prepared by adding 208 grams of $Na_2HPO_4$ (Mol. wt. 142) and 71 grams of $NaH_2PO_4$ (Mol. wt. 120) in water. If the $pK_a$ for the dissociation of $H_2PO_4^-$ into $HPO_4^{2–}$ and $H^+$ is 6.86, the pH of the buffer will be __________
