Question

A hot air balloon can have a volume of 2950 cubic meters (2.95 ✕ 106 liters) and operate at temperatures up to 250°F (121°C). Assuming a balloon is operating at this maximum temperature with an external pressure of 1.00 atm, what mass of air would the balloon hold? While air is a mixture of many gases, we can assume a molar mass of 28.97 g/mol for air.

Answer 1

Answer:

2.64 × 10⁶ g

Explanation:

We can find the mass of air using the ideal gas equation.

$P.V=n.R.T=\frac{m}{M} .R.T$

where,

P is the pressure (P = 1.00 atm)

V is the volume (V = 2.95 × 10⁶ L)

n is the number of moles

R is the ideal gas constant (0.08206atm.L/mol.K)

T is the absolute temperature (121°C + 273 = 394 K)

m is the mass

M is the molar mass (28.09 g/mol)

$m=\frac{P.V.M}{R.T} =\frac{1.00atm \times 2.95 \times 10^{6} L \times 28.97g/mol}{(0.08206atm.L/mol.K) \times 394 K } =2.64 \times 10^{6} g$