Question

The CO2 that builds up in the air of a submerged submarine can be removed by reacting it with sodium peroxide. 2 Na2O2 (s) + 2 CO2 (g) → 2 Na2CO3 (s) + O2 (g)
If a sailor exhales 150.0 mL of CO2 per minute at 20oC and 1.02 atm, how much sodium peroxide is needed per sailor in a 24 hr period?​

Answer 1

Answer: The sodium peroxide needed per sailor in a 24 hr period is 674 grams.

Explanation:

According to ideal gas equation:

$PV=nRT$

P = pressure of gas = 1.02 atm

V = Volume of gas = 150.0 ml = 0.15 L

n = number of moles  of carbon dioxide = ?

R = gas constant =$0.0821Latm/Kmol$

T =temperature =$20^0C=(20+273)K=293K$

$n=\frac{PV}{RT}$

$n=\frac{1.02atm\times 0.15L}{0.0821 L atm/K mol\times 293K}=0.006moles$

$2Na_2O_2(s)+2CO_2(g)\rightarrow 2Na_2CO_3(s)+O_2(g)$

According to stoichiometry:

2 moles of carbon dioxide require = 2 moles of sodium peroxide

Thus 0.006 moles carbon dioxide require= $\frac{2}{2}\times 0.006=0.006$ moles of  sodium peroxide

Mass of  sodium peroxide needed for 24 hour=$moles\times {\text {Molar mass}}=0.006mol\times 78g/mol\times 24\times 60=674g$

Thus sodium peroxide needed per sailor in a 24 hr period is 674 grams.