Q.7.56 - An Introduction to General, Organic, and Biological Chemistry

Question

Ammonia is produced by the chemical reaction of hydrogen and nitrogen.

${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\to 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$

a. How many moles of H₂ are needed to react with 1.8 moles of N₂?

b. How many moles of N₂ reacted if 0.60 moles of NH₃ is produced?

c. How many moles of NH₃ are produced when 1.4 moles of H₂ react?

Step-by-Step Solution

Answer

a. 5.4 moles of H₂ are needed to react with 1.8 moles of N₂ .

b. 0.3 moles of N₂ reacted if 0.60 moles of NH₃ is produced.

c. 0.933 moles of NH₃ are produced when 1.4 moles of H₂ react.

Step 1: Given information

The moles of N₂ are 1.8 moles.

Step 2: Part (a) Explanation

The balanced chemical reaction is given as follows:

${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\to 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$

From the equation, it is observed that  1 mole of nitrogen gas reacts with three moles of hydrogen to produce 2 moles of ammonia.

Thus, to calculate the number of moles of hydrogen needed if 1.8 moles of Nitrogen react, the following conversation takes place.

$\frac{3 \mathrm{moles} {\mathrm{H}}_2}{1 \mathrm{mole} {\mathrm{N}}_2} \mathrm{and} \frac{1 \mathrm{mole} {\mathrm{N}}_2}{3 \mathrm{moles} {\mathrm{H}}_2}$

Therefore, the number of moles of hydrogen are:

$1.8 \cancel{\mathrm{moles} {\mathrm{N}}_2}\times \frac{3 \mathrm{mole}s {\mathrm{H}}_2}{1 \cancel{\mathrm{mole} {\mathrm{N}}_2}}=1.8\times 3=5.4 \mathrm{mole}s {\mathrm{H}}_2$

Hence, 5.4 moles of H₂ are needed to react with 1.8 moles of N₂ .

Step 1: Part (b) Given Information

The moles of ammonia that are produced are 0.60 moles.

Step 2: Part (b) Explanation

The balanced chemical reaction is given as follows:

${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\to 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$

From the equation, it is observed that  1 mole of nitrogen gas reacts with three moles of hydrogen to produce 2 moles of ammonia.

Thus, to calculate the number of moles of nitrogen needed if 0.60 moles of ammonia is produced, the following conversation takes place.

$\frac{1 \mathrm{mole} {\mathrm{N}}_2}{2 \mathrm{moles} {\mathrm{NH}}_3} \mathrm{and} \frac{2 \mathrm{moles} {\mathrm{NH}}_3}{1 \mathrm{mole} {\mathrm{N}}_2}$

Therefore, if 0.60 moles of NH₃ is produced, the moles of nitrogen will be:

$0.60 \cancel{\mathrm{moles} {\mathrm{NH}}_3}\times \frac{1 \mathrm{mole} {\mathrm{N}}_2}{2 \cancel{\mathrm{moles} {\mathrm{NH}}_3}}=0.3 \mathrm{moles} {\mathrm{NH}}_3$

Hence, 0.3 moles of N₂ reacted if 0.60 moles of NH₃ is produced.

Step 1: Part (c) Given Information

The moles of H₂ are 1.4 moles.

Step 2: Part (c) Explanation

The balanced chemical reaction is given as follows:

${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\to 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$

From the equation, it is observed that  1 mole of nitrogen gas reacts with three moles of hydrogen to produce 2 moles of ammonia.

Thus, to calculate the number of moles of ammonia needed if 1.4 moles of hydrogen react, the following conversation takes place.

$\frac{3 \mathrm{moles} {\mathrm{H}}_2}{2 \mathrm{moles} {\mathrm{NH}}_3} \mathrm{and} \frac{2 \mathrm{moles} {\mathrm{NH}}_3}{3 \mathrm{moles} {\mathrm{H}}_2}$

Therefore, for 1.4 moles of H₂  , the moles of ammonia are:

$1.4 \cancel{\mathrm{moles} {\mathrm{H}}_2}\times \frac{2 \mathrm{moles} {\mathrm{NH}}_3}{3 \cancel{\mathrm{moles} {\mathrm{H}}_2}}=\frac{1.4\times 2 \mathrm{moles} {\mathrm{NH}}_3}{3}=0.933 \mathrm{moles} {\mathrm{NH}}_3$

Hence, 0.933 moles of NH₃ are produced when 1.4 moles of H₂ react.