Question

Chloral hydrate $\left(C_{12}{H}_{13}{\mathrm{Cl}}_3{O}_2\right)$is a drug formerly used as a sedative and hypnotic. It is the compound used to make “Mickey Finns” in detective stories.

a. Calculate the molar mass of chloral hydrate.

b. How many moles of $\mathbf{\left(}{\mathbf{C}}_{\mathbf{12}}{\mathbf{H}}_{\mathbf{13}}{\mathbf{Cl}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{2}}\mathbf{\right)}$ molecules are in 500.0 g of chloral hydrate?

c. What is the mass in grams of $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$ mol chloral hydrate?

d. How many chlorine atoms are in 5.0 g chloral hydrate?

e. What mass of chloral hydrate would contain 1.0 g Cl?

f. What is the mass of exactly 500 molecules of chloral hydrate?

g. What mass of chloral hydrate would contain 12.0 g Cl?

Short answer

a. The molar mass is$165.403\mathrm{g}/\mathrm{mol}$

b. The moles are 3.0229 mol.

c. The mass is 3.30806 g.

d. The moles are$0.5462\times {10}^{23}\mathrm{Atoms}$

e. The mass is 1.555 g.

f. The mass is$13.7010\times {10}^{-20}\mathrm{g}$

g. The mass is 1.555 g.

Step-by-step solution

Definition of molar mass

A molar mass of a chemical compound is the mass of a sample of the compound divided by the amount of substance.

a. Calculation of Chloral hydrate molar mass

$$\begin{gathered} =2\times 12.011+3\times 1.008+3\times 35.453+2\times 15.999 \\ =28.012+3.024+106.359+31.998 \\ =165.403\mathrm{g}/\mathrm{mol} \end{gathered}$$

Hence, the Chloral hydrate molar mass is$165.403\mathrm{g}/\mathrm{mol}$

b. Calculation of moles

$$\begin{gathered} =\frac{\mathrm{Mass}}{\mathrm{Molar}\mathrm{mass}} \\ =\frac{500.0\mathrm{g}}{165.403\mathrm{g}/\mathrm{mol}} \\ =3.0229\mathrm{mol} \end{gathered}$$

c. Calculation of mass

$$\begin{gathered} =\mathrm{number}\mathrm{of}\mathrm{moles}\times \mathrm{molar}\mathrm{mass} \\ =165.403\mathrm{g}/\mathrm{mol}\times 2.0\times {10}^{-2}\mathrm{mol} \\ =3.30806\mathrm{g} \end{gathered}$$

d. Calculation of moles

5 g of moles as,

$$\begin{gathered} =\frac{5\mathrm{g}}{165.403\mathrm{g}/\mathrm{mol}} \\ =0.03022\mathrm{moles} \end{gathered}$$

1 mole of chloral hydrate is equal to the 3 moles of chlorine atoms.

Now,

$$\begin{gathered} =3\times 0.030229\mathrm{moles}\mathrm{of}\mathrm{Cl}\mathrm{atoms} \\ =3\times 0.030229\times 6.023\times {10}^{23}\mathrm{atoms} \\ =0.5462\times {10}^{23}\mathrm{Atoms} \end{gathered}$$

Hence, the mole of the chlorine atom is$0.5462\times {10}^{23}\mathrm{Atoms}$

e. Calculation of mass

The chlorine mole as,

$$\begin{gathered} =\frac{\mathrm{Mass}}{\mathrm{Atomic}\mathrm{mass}} \\ =\frac{1.0\mathrm{g}}{35.453} \\ =0.0282\mathrm{moles}\mathrm{of}\mathrm{Cl} \end{gathered}$$

The one-mole chloral hydrate is equal to the 3 moles of Cl.

Now,

The Cl moles is given as:

$$\begin{gathered} =\frac{0.0282}{3} \\ =0.0094\mathrm{moles}\mathrm{of}\mathrm{chloral}\mathrm{hydrate} \end{gathered}$$

Hence, the mass is found as:

$$\begin{gathered} =0.0094\mathrm{mol}\times 165.403\mathrm{g}/\mathrm{mol} \\ =1.555\mathrm{g} \end{gathered}$$

f. Calculation of mass

For 500 molecules,

$$\begin{gathered} =\frac{500}{6.023\times {10}^{23}}\mathrm{moles} \\ =83.015\times {10}^{-23}\mathrm{moles} \end{gathered}$$

Hence, the mass as:

$$\begin{gathered} =83.015\times {10}^{-23}\times 165.403\mathrm{g}/\mathrm{mol} \\ =13.7010\times {10}^{-20}\mathrm{g} \end{gathered}$$

e. Calculation of mass

The chlorine mole as:

$$\begin{gathered} =\frac{\mathrm{Mass}}{\mathrm{Atomic}\mathrm{mass}} \\ =\frac{1.0\mathrm{g}}{35.453} \\ =0.0282\mathrm{moles}\mathrm{of}\mathrm{Cl} \end{gathered}$$

The one-mole chloral hydrate is equal to the3 moles of Cl.