Respuesta :
Answer: The sodium peroxide needed per sailor in a 24 hr period is 674 grams.
Explanation:
According to ideal gas equation:
[tex]PV=nRT[/tex]
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 =[tex]0.0821Latm/Kmol[/tex]
T =temperature =[tex]20^0C=(20+273)K=293K[/tex]
[tex]n=\frac{PV}{RT}[/tex]
[tex]n=\frac{1.02atm\times 0.15L}{0.0821 L atm/K mol\times 293K}=0.006moles[/tex]
[tex]2Na_2O_2(s)+2CO_2(g)\rightarrow 2Na_2CO_3(s)+O_2(g)[/tex]
According to stoichiometry:
2 moles of carbon dioxide require = 2 moles of sodium peroxide
Thus 0.006 moles carbon dioxide require= [tex]\frac{2}{2}\times 0.006=0.006[/tex] moles of sodium peroxide
Mass of sodium peroxide needed for 24 hour=[tex]moles\times {\text {Molar mass}}=0.006mol\times 78g/mol\times 24\times 60=674g[/tex]
Thus sodium peroxide needed per sailor in a 24 hr period is 674 grams.
The amount (in grams) of sodium peroxide needed per sailor in a 24 hr period is 673.92 g
Determination of the mole of CO₂
- Volume (V) = 150 mL = 150 / 1000 = 0.15 L
- Temperature (T) = 20 °C = 20 + 273 = 293 K
- Pressure (P) = 1.02 atm
- Gas constant (R) = 0.0821 atm.L/Kmol
- Mole of CO₂ (n) =?
Using the ideal gas equation, we can obtain the mole of CO₂ as follow:
n = PV / RT
n = (1.02 × 0.15) / (0.0821 × 293)
n = 0.006 mole
How to determine the mole of Na₂O₂ required
2Na₂O₂ + 2CO₂ → 2Na₂CO₃ + O₂
From the balanced equation above,
2 moles of CO₂ required 2 moles of Na₂O₂.
Therefore,
0.006 mole of CO₂ will also require 0.006 mole of Na₂O₂.
How to determine the mass of Na₂O₂ required
- Mole of Na₂O₂ = 0.006 mole
- Molar mass of Na₂O₂ = (23×2) + (16×2) = 78 g/mol
- Mass of Na₂O₂ =?
Mass = mole × molar mass
Mass of Na₂O₂ = 0.006 × 78
Mass of Na₂O₂ = 0.468 g per minute
Mass of Na₂O₂ required for 24 h = 0.468 × 24 × 60 = 673.92 g
Learn more about stoichiometry:
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