Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, t1/2=3.00 hours. What fraction of sample of sucrose remains after 8 hours?

# Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, ${\mathrm{t}}_{1/2}=3.00$ hours. What fraction of sample of sucrose remains after 8 hours?

1. A

1.158M

2. B

0.518M

3. C

0.158M

4. D

3.182M

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### Solution:

${\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}+{\mathrm{H}}_{2}\mathrm{O}\stackrel{{\mathrm{H}}^{+}}{\to }{\mathrm{C}}_{6}{\mathrm{H}}_{12}{\mathrm{O}}_{6}+{\mathrm{C}}_{6}{\mathrm{H}}_{12}{\mathrm{O}}_{6}$

It was ${1}^{\mathrm{st}}$ order reaction

for ${\mathrm{t}}_{1/2}=\frac{0.693}{\mathrm{k}}$

$\left[\mathrm{A}\right]=1-x$

$\frac{1}{1-\mathrm{X}}={10}^{0.8024}=6.3445$

$1-\mathrm{X}=\frac{1}{6.2445}=0.158\mathrm{M}$

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