Question

18. A bag of potato chips contains 585 mL of air at 0.998 atm and 28°C. Assuming the bag does not break, what will be its volume at the top of a mountain where the pressure has dropped to 445 mmHg and 5.4°C? 19. Nitrogen reacts with powdered aluminum according to the following chemical equation: 2 Al (s)+N2 (g)2 AIN (s) How many liters of nitrogen gas are required to react with 22.3 g of powdered aluminum if the reaction occurs at 825 torr and 89°C?

Answer 1

Q18. According to combined gas law,

(P1 * V1) / T1 = (P2 * V2) / T2

where

P1 = initial pressure = 0.998 atm

V1 = initial volume = 585 mL

T1 = initial temperature = 28^oC = (28 + 273) K = 301 K

P2 = final pressure = 445 mmHg = 445 mmHg * (1 atm / 760 mmHg) = 0.5855 atm

V2 = final volume

T2 = final temperature = 5.4^oC = (5.4 + 273) K = 278.4 K

Substituting the values,

(0.998 atm * 585 mL) / (301 K) = (0.5855 atm * V2) / (278.4 K)

V2 = 585 mL * (0.998 atm / 0.5855 atm) * (278.4 K / 301 K)

V2 = 585 mL * (1.576)

V2 = 922 mL

volume at top of the mountain will be 922 mL

Q19. mass of aluminum = 22.3 g

moles Al = (mass Al) / (molar mass Al)

moles Al = (22.3 g) / (27.0 g/mol)

moles Al = 0.826 mol

moles N₂ required = (moles Al) * (1 mole N₂ / 2 moles Al)

moles N₂ required = (0.826 mol) * (1/2)

moles N₂ required = (0.826 mol) * (0.5)

moles N₂ required = 0.413 mol

According to ideal gas law,

V = [(n) * (R) * (T)] / (P)

where V = volume of N₂ required

n = moles N₂ required = 0.413 mol

R = gas constant = 0.0821 L-atm/mol-K

T = temperature = 89^oC = (89 + 273) K = 362 K

P = pressure = 825 torr = 825 torr * (1 atm / 760 torr) = 1.0855 atm

Substituting the values,

Volume of N₂ required = [(0.413 mol) * (0.0821 L-atm/mol-K) * (362 K)] / (1.0855 atm)

Volume of N₂ required = 11.3 L