Q. 7.114 - An Introduction to General, Organic, and Biological Chemistry

Question

Ammonium sulfate, ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{SO}}_4$, is used in fertilizers to provide nitrogen for the soil.
a. How many formula units are in $0.200$ mole of ammonium sulfate?
b. How many $\mathrm{H}$ atoms are in $0.100$ mole of ammonium sulfate?
c. How many moles of ammonium sulfate contain $7.4\times {10}^{25}$ atoms of $\mathrm{N}$ ?
d. What is the molar mass of ammonium sulfate?

Step-by-Step Solution

Answer

Part(a) $1.2\times {10}^{23}$ formula units are in $0.200$ mole of ammonium sulfate

Part(b) $4.96\times {10}^{23}$ $\mathrm{H}$ atoms are in $0.100$ mole of ammonium sulfate

Part(c)  $59.7$ moles of ammonium sulfate contain $7.4\times {10}^{25}$ atoms of $\mathrm{N}$ 

Part(d)  Molar mass of ammonium sulfate is $132$

Part(a) Step 1 : Given information

We are given that Ammonium sulfate is used in fertilizers to provide nitrogen for the soil.

Part(a) Step 2 : Simplify

As we know one mole of ammonium sulfate has $6.02\times {10}^{23}$ formula units.

Therefore $0.200$ mole of ammonium sulfate has $0.2 \mathrm{moles}\times 6.02\times {10}^{23}=1.2\times {10}^{23} \mathrm{units}$ .

Part(b) Step 1 : Given information

We are given that Ammonium sulfate is used in fertilizers to provide nitrogen for the soil.

Part(b) Step 2 : Simplify

As we know one mole of ammonium sulfate contains eight mole of hydrogen atoms.

Therefore $0.100$ mole of ammonium sulfate contains $0.100 \mathrm{moles}\times 8\times 6.2\times {10}^{23}=4.96\times {10}^{23} \mathrm{atoms}$ of hydrogen.

Part(c) Step 1 : Given information

We are given that Ammonium sulfate is used in fertilizers to provide nitrogen for the soil.

Part(c) Step 2 : Simplify

As we know one mole of ammonium sulfate contains two mole of nitrogen atom. 

Therefore, $7.4\times {10}^{25}$ atoms of nitrogen contains $7.4\times {10}^{25}\times \frac{1}{2}\times \frac{1}{6.2\times {10}^{23}}=59.7 \mathrm{moles}$ of ammonium sulfate.

Part(d) Step 1 : Given information

We are given that Ammonium sulfate is used in fertilizers to provide nitrogen for the soil.

Part(d) Step 2 : Simplify

As we know , molar mass of $\mathrm{N}=14$, $\mathrm{H}=1$, $\mathrm{S}=32$, $\mathrm{O}=16$

According to formula molar mass of ammonium sulphate $\left(14\times 2\right) \mathrm{g}+\left(1\times 8\right) \mathrm{g}+\left(32\times 1\right) \mathrm{g}+\left(16\times 4\right) \mathrm{g}=132 \mathrm{g}$