Consider this reaction:
2H, PO₂ (aq)-P₂O, (aq) + 3H₂O (aq)
At a certain temperature it obeys this rate law.
rate - (0.221 s¹)[H₂PO4]
Suppose a vessel contains H₂PO, at a concentration of 1.30 M. Calculate how long it takes for the concentration of H₂PO4 to
decrease to 15.0% of its initial value. You may assume no other reaction is important.
Round your answer to 2 significant digits.
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To solve this problem, we can use the integrated rate law for a first-order reaction:
ln([H₂PO₄]₀/[H₂PO₄]) = kt
Where [H₂PO₄]₀ is the initial concentration of H₂PO₄, [H₂PO₄] is the concentration of H₂PO₄ at time t, k is the rate constant, and t is the time.
Let's rearrange the equation and solve for t:
kt = ln([H₂PO₄]₀/[H₂PO₄])
t = ln([H₂PO₄]₀/[H₂PO₄])/k
Given that the rate constant is 0.221 s⁻¹, we can plug in the values:
t = ln(1.30 M / 0.15 M) / 0.221 s⁻¹
The concentration of H₂PO₄ decreases to 15% of its initial value, so [H₂PO₄] = 0.15 M.
t = ln(1.30 M / 0.15 M) / 0.221 s⁻¹
Using a calculator, we find:
t ≈ 7.35 s
Therefore, it takes approximately 7.35 seconds for the concentration of H₂PO₄ to decrease to 15% of its initial value.