# Consider the reaction ${\mathrm{N}}_{2}\left(\mathrm{g}\right)+3{\mathrm{H}}_{2}\left(\mathrm{g}\right)\to 2{\mathrm{NH}}_{3}\left(\mathrm{g}\right)$The equality relationship between

1. A

$+\frac{\mathrm{d}\left[{\mathrm{NH}}_{3}\right]}{\mathrm{dt}}=-\frac{2}{3}\frac{\mathrm{d}\left[{\mathrm{H}}_{2}\right]}{\mathrm{dt}}$

2. B

$+\frac{\mathrm{d}\left[{\mathrm{NH}}_{3}\right]}{\mathrm{dt}}=-\frac{3}{2}\frac{\mathrm{d}\left[{\mathrm{H}}_{2}\right]}{\mathrm{dt}}$

3. C

$\frac{\mathrm{d}\left[{\mathrm{NH}}_{3}\right]}{\mathrm{dt}}=-\frac{\mathrm{d}\left[{\mathrm{H}}_{2}\right]}{\mathrm{dt}}$

4. D

$\frac{\mathrm{d}\left[{\mathrm{NH}}_{3}\right]}{\mathrm{dt}}=-\frac{1}{3}\frac{\mathrm{d}\left[{\mathrm{H}}_{2}\right]}{\mathrm{dt}}$

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### Solution:

If we write rate of reaction in terms of concentration of

Rate of reaction  $=\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{NH}}_{3}\right]}{\mathrm{dt}}=-\frac{1}{3}\frac{\mathrm{d}\left[{\mathrm{H}}_{2}\right]}{\mathrm{dt}}$
So $\frac{\mathrm{d}\left[{\mathrm{NH}}_{3}\right]}{\mathrm{dt}}=-\frac{2}{3}\frac{\mathrm{d}\left[{\mathrm{H}}_{2}\right]}{\mathrm{dt}}$

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