AP EAMCET · Chemistry · Chemical Kinetics

For an elementary reaction, $X_{(g)} ⟶ Y_{(g)} + Z_{(g)}$ , the $t_{1 / 2}$ is $10$ minutes. In what period of time would the concentration of $X$ be reduced to $10 %$ of its original concentration?

A $20 minutes$
B $33.2 minutes$
C $15 minutes$
D $25.2 minutes$

Verified Solution

Answer & Solution

Correct Answer

(B) $33.2 minutes$

Step-by-step Solution

Detailed explanation

X(g)⟶Y(g)+Z(g) Let the concentration at t=0 = x The concentration after time t=t = a-x=10%x = 0.1x K=0.693t12=0.69310=0.0693 According to the integrated rate law, t=1Klnaa-x=10.0693ln10.1=10.0693ln10=2.3030.0693=33.2 Hence, the time is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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For an elementary reaction, X(g)⟶Y(g)+Z(g), the t1/2 is 10 minutes. In what period of time would the concentration of X be reduced to 10% of its original concentration?

Step-by-step Solution

For an elementary reaction, $X_{(g)} ⟶ Y_{(g)} + Z_{(g)}$ , the $t_{1 / 2}$ is $10$ minutes. In what period of time would the concentration of $X$ be reduced to $10 %$ of its original concentration?