Question

The decomposition of formic acid follows first-order kinetics. HCO2H(g) → CO2(g) + H2(g) The half-life for the reaction at 550°C is 24 seconds. How many seconds does it take for the formic acid concentration to decrease by 87.5%? (1) 4.6 seconds (2) 36 seconds (3) 48 seconds (4) 72 seconds (5) 96 seconds

Answer 1

Answer:

Option 4 is correct (72 seconds)

Explanation:

Option 4 is correct (72 seconds)

The formula we are going to use is:

$ln\frac{A}{A_o}=-kt$

Where:

A is the final concentration

A_o is the initial concentration

k is the constant

t is the time

Half-Life=0.693/k

Half-life in our case=24 seconds

k=0.693/24

k=0.028875 s^-1

Since the concentration is decreased by 87.5 % which means only 12.5%(100-87.5%) is left.

The ratio $A/A_o$ will become 0.125

$ln 0.125=-0.028875*t\\t=72.015\ seconds$

t≅ 72 seconds