An ideal gas at 12.1 °C and a pressure of 2.38 x 105 Pa occupies a volume of 2.88 m3. (a) How many moles of gas are present? (b) If the volume is raised to 4.70 m3 and the temperature raised to 28.3 °C, what will be the pressure of the gas?
To calculate the number of moles of gas present, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant (8.314 J/mol·K)
T is the temperature in Kelvin
Let's solve part (a) first:
(a) To calculate the number of moles of gas, we can rearrange the ideal gas law equation to solve for n:
n = PV / RT
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
Given:
Temperature (T) = 12.1 °C = 12.1 + 273.15 = 285.25 K
Pressure (P) = 2.38 x 10^5 Pa
Volume (V) = 2.88 m^3
Ideal gas constant (R) = 8.314 J/mol·K
Now, substitute the given values into the equation:
n = (2.38 x 10^5 Pa) * (2.88 m^3) / (8.314 J/mol·K) * (285.25 K)
Simplifying the equation:
n ≈ 29.7 mol
Therefore, there are approximately 29.7 moles of gas present.
Now, let's move on to part (b):
(b) In this part, we need to calculate the new pressure of the gas when the volume increases to 4.70 m^3 and the temperature increases to 28.3 °C.
First, convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
Given:
Temperature (T) = 28.3 °C = 28.3 + 273.15 = 301.45 K
Volume (V) = 4.70 m^3
Now, we can use the ideal gas law equation again to solve for the new pressure:
P2 = (n * R * T2) / V2
Substituting the given values:
P2 = (29.7 mol * 8.314 J/mol·K * 301.45 K) / 4.70 m^3
Simplifying the equation:
P2 ≈ 508844 Pa
Therefore, the pressure of the gas at the new conditions is approximately 508844 Pa.