Question

diphenhydramine hydrochloride, a drug used commonly as an antihistamine, has the formula ( c_{17}h_{21}nocdot hcl ). what is the percent composition of each element in this compound?
carbon:
%
hydrogen:
%
nitrogen:
%
oxygen:
%
chlorine:
%

Explanation:

Step1: Calculate molar mass of each element

• Molar mass of \(C = 12.01\ g/mol\), \(H = 1.008\ g/mol\), \(N = 14.01\ g/mol\), \(O = 16.00\ g/mol\), \(Cl = 35.45\ g/mol\)
• For \(C_{17}H_{21}NO\cdot HCl\), total \(C = 17\), \(H=21 + 1=22\), \(N = 1\), \(O = 1\), \(Cl = 1\)
• Molar mass of compound \(M=(17\times12.01)+(22\times1.008)+14.01 + 16.00+35.45\)

\(M = 204.17+22.176+14.01+16.00+35.45=291.706\ g/mol\)

Step2: Calculate percent composition

• Carbon:

\(\text{Percent of }C=\frac{17\times12.01}{291.706}\times100\%=\frac{204.17}{291.706}\times100\%\approx69.99\%\)

• Hydrogen:

\(\text{Percent of }H=\frac{22\times1.008}{291.706}\times100\%=\frac{22.176}{291.706}\times100\%\approx7.60\%\)

• Nitrogen:

\(\text{Percent of }N=\frac{14.01}{291.706}\times100\%\approx4.80\%\)

• Oxygen:

\(\text{Percent of }O=\frac{16.00}{291.706}\times100\%\approx5.49\%\)

• Chlorine:

\(\text{Percent of }Cl=\frac{35.45}{291.706}\times100\%\approx12.15\%\)

Answer:

carbon: \(69.99\%\)
hydrogen: \(7.60\%\)
nitrogen: \(4.80\%\)
oxygen: \(5.49\%\)
chlorine: \(12.15\%\)