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 [tex]97^{o}C[/tex].
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.
[tex]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[/tex]
Hence, temperature of this gas is 1032.88 K.
2). Given: Pressure = 14.5 atm
Volume = 45 L
Temperature = [tex]97^{o}C = (97 + 273) K = 370 K[/tex]
Formula used to calculate number of moles is as follows.
[tex]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[/tex]
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 [tex]97^{o}C[/tex].
