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?

Short 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 $132$

Step-by-step solution

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 $\left(14\times 2\right)\mathrm{g}+\left(1\times 8\right)\mathrm{g}+\left(32\times 1\right)\mathrm{g}+\left(16\times 4\right)\mathrm{g}=132\mathrm{g}$