Answer to Question #135955 in Physical Chemistry for Brianne Lake

Question

A 22.5 mL sample of liquid ethanol (C₂H₅OH, density = 0.789 g/mL) was injected into a 10.0 L cylinder containing O₂ at a pressure of 4.50 atm and a temperature of 25°C. The cylinder was heated to 125°C and a spark was used to ignite the ethanol, which was completely combusted. What was the final total pressure in the cylinder (in atm) after the reaction, while it was still at 125°C?

Answer 1

$C_2H_5OH + 3O_2 \rightarrow 2CO_2 + 3H_2O$

1) find moles of ethanol

$22.5 ml \times (\frac{0.789g}{1 ml})\times(\frac{1 mole}{46.07 g})= 0.385 moles (C_2H_5OH)$

2) find moles of O2. Use Ideal Gas Law

$PV=nRT$

$n=\frac{PV}{RT}=\frac{4.50 atm\times 10.0 L}{0.082\frac{l \times atm}{mol\times K}\times(273+25)}= 1.84 moles$

3) Find limiting reagent

$\frac{0.385 moles (C_2H_5OH)}{1}<\frac{1.84 moles (O_2)}{3}$

C$_2H_5OH$ - limiting reactant

4) Find moles of O2 after reaction

The moles of O2 consumed in the reaction:

$0.386 moles (C_2H_5OH)\times \frac{3 moles (O_2)}{1 mole (C_2H_5OH)}=1.16 moles (O_2)$

The moles of O2 left after the recation was completed:

$1.84 moles (O_2) - 1.16 moles (O_2)=0.68 moles (O_2)$

5) Find moles of CO2

$0.386 moles (C_2H_5OH)\times(\frac{2 moles (CO_2)}{1 mole (C_2H_5OH)})=0.772 moles (CO_2)$

6) Find moles of H2O

$0.386 moles (C_2H_5OH)\times (\frac{3 moles (H_2O)}{1 mole (C_2H_5OH)})= 1.16 moles (H_2O)$

7) Find the total munber of moles of gases:

$0.68+0.772+1.16 = 2.612 moles$

8) Find total pressure:

$PV=nRT$

$P=\frac{nRT}{V}=\frac{2.162 moles\times0.082\frac{L\times atm}{mol\times K}\times(273+125)}{10.0 L}= 7.06 atm$