Question

If I have 6 moles of a gas at a pressure of 10.6 atm and a volume of 48 liters, what is the temperature of this gas?

Answer 1

Answer: 1). The temperature of this gas is 1032.88 K.

2). There are 21.48 moles of gas exist at a pressure of 14.5 atm, a volume of 45 liters, and a temperature of $97^{o}C$.

Explanation:

1). Given: No. of moles = 6 moles

Pressure = 10.6 atm

Volume = 48 L

Formula used to calculate temperature is as follows.

PV = nRT

where,

P = pressure

V = volume

n = no. of moles

R = gas constant = 0.0821 atm

T = temperature

Substitute the values into above formula as follows.

$PV = nRT\\10.6 atm \times 48 L = 6 mol \times 0.0821 L atm/mol K \times T\\T = \frac{10.6 atm \times 48 L}{6 mol \times 0.0821 L atm/mol K}\\= \frac{508.8}{0.4926} K\\= 1032.88 K$

Hence, temperature of this gas is 1032.88 K.

2). Given: Pressure = 14.5 atm

Volume = 45 L

Temperature = $97^{o}C = (97 + 273) K = 370 K$

Formula used to calculate number of moles is as follows.

$PV = nRT\\14.5 atm \times 45 L = n \times 0.0821 L atm/mol K \times 370 K\\n = \frac{14.5 atm \times 45 L}{0.0821 L atm/mol K \times 370 K}\\= \frac{652.5}{30.377} mol\\= 21.48 mol$

Hence, there are 21.48 moles of gas exist at a pressure of 14.5 atm, a volume of 45 liters, and a temperature of $97^{o}C$.