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?

An unknown quantity of gas is at a pressure of 14.5 atm, a volume of 45 liters, and a temperature of 97 0C, how many moles of gas exist in this situation?

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`.

Step-by-step 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 * 48 L = 6 mol * 0.0821 L atm/mol K * T\\T = (10.6 atm * 48 L)/(6 mol * 0.0821 L atm/mol K)\\= (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 * 45 L = n * 0.0821 L atm/mol K * 370 K\\n = (14.5 atm * 45 L)/(0.0821 L atm/mol K * 370 K)\\= (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`.