How much salicylic acid is required to produce 1.5x10^2 kg of aspirin, assuming only 80 percent of the salicylic acid is converted to aspirin?

The balanced chemical reaction for conversion of salicylic acid to aspirin is as follows:

C_{7}H_{6}O_{3}+C_{4}H_{6}O_{3}\rightarrow C_{9}H_{8}O_{4}+HC_{2}H_{3}O_{2}

From the above reaction 1 mol of salicylic acid gives 1 mol of aspirin. Now, 1.5\times 10^{2} kg of aspirin is produced. First convert this into number of moles.

Molar mass of aspirin is 180.157 g/mol, thus,

n=\frac{m}{M}=\frac{1.5\times 10^{2} kg}{180.157 g/mol}

converting mass into grams,

n=\frac{m}{M}=\frac{1.5\times 10^{5} kg}{180.157 g/mol}=2.70\times 10^{7} mol

thus, moles of salicylic acid required will also be 2.70\times 10^{7} mol. Converting moles into mass as follows:

m=n×M

molar mass of salicylic acid is 138.121 g/mol

thus, m=2.70\times 10^{7} mol×138.121 g/mol=3.73\times 10^{9} g

or,

3.73\times 10^{6} kg

This is the mass produced if 100% of salicylic acid is converted into aspirin. Now, if only 80% of salicylic acid is converted into aspirin then the mass of salicylic acid used (let x) can be calculated as follows:

80% of x=3.73\times 10^{6}

Or,\frac{80}{100}\times x=3.73\times 10^{6}

x=3.73\times 10^{6}kg\times \frac{100}{80}=4.66\times 10^{6} kg

Thus, mass of salicylic acid required will be 4.66\times 10^{6} kg.