A room has a volume of 50 m³ and is filled with air of an average molecular mass of 29 u.What is the mass of the air in the room at a pressure of 1.0 atm and temperature of 25°C? R = 0.082 L⋅atm/mol⋅K

Question

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First, we need to convert the room's volume from m^3 to L by multiplying by 1000, giving us 50000 L. Then we can use the ideal gas law to calculate the mass of the air in the room.

PV = nRT

n = moles of air = PV/RT

We know the pressure (1.0 atm), temperature (25°C = 298 K), volume (50000 L), and universal gas constant (R = 0.082 L•atm/mol•K).

n = (1.0 atm) x (50000 L) / [(0.082 L•atm/mol•K) x (298 K)]

n = 2012.7 moles of air

Finally, we can calculate the mass of air using the molar mass of air (29 g/mol) and the number of moles we just found:

mass = n x molar mass

mass = (2012.7 mol) x (29 g/mol)

mass = 58384.3 g or 58.3843 kg

Rounding to two significant figures, we get:

Answer: C (59 kg)

A Room Has a Volume of 50 M3 and Is

A Room Has a Volume of 50 M³ and Is