An ideal gas at 19.8 °C and a pressure of 2.79 x 105 Pa occupies a volume of 3.66 m3. (a) How many moles of gas are present? (b) If the volume is raised to 7.20 m3 and the temperature raised to 28.5 °C, what will be the pressure of the gas?
I got a) right with 419.46, but im stuck on part b) I replaced T with 301.65(converted to Kelvin) and V with 7.20 but I got 3689.3 which is wrong. Where did I go wrong ?
Solve for n in PV=nRT
2.79*10^5(3.66)=n×8.314462175×(19.8+273.15)
to get
419 moles (3 sig. figures)
and similarly solve for P in
P(7.20)=419.235(8.314462175)(28.5+273.15)
to get 1.46*10^5 (3 sig. figures)
Your approach is correct, but cannot tell where you got wrong without seeing your calculations.
To solve part b) of the question, you need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = Temperature in Kelvin
Let's go through the steps to solve the problem correctly:
Step 1: Convert the given temperature to Kelvin.
Given: Temperature (T) = 28.5 °C
To convert Celsius to Kelvin, use the equation:
Kelvin = Celsius + 273.15
So, Temperature (T) in Kelvin = 28.5 + 273.15 = 301.65 K
You have correctly converted the temperature to Kelvin.
Step 2: Calculate the new pressure.
Given: Volume (V) = 7.20 m³
Using the equation PV = nRT, we can rearrange it to solve for pressure (P):
P = (nRT) / V
Substituting the given values:
P = (419.46 moles x 8.314 J/(mol·K) x 301.65 K) / 7.20 m³
Calculating the above expression using a calculator:
P = 10106.23 Pa
So, the pressure of the gas at the new conditions will be approximately 10106.23 Pa.
Note: Pay attention to the units you are using. Make sure all the units are consistent throughout the calculation. In this case, the volume is given in cubic meters (m³), so the pressure must be in pascals (Pa).