What is the volume of 14 mol of ideal gas if its pressure is 233 kPa and its
temperature is 140 ºC? (1 mol of ideal gas at STP occupies 22.4 L).
I would use PV = nRT. You know n, R, T, and P. Solve for V. Or you may use the other bit of information given that 1 mol at STP occupies 22.4L.
So you know that at STP you will have 14 x 22.4L, then use
(p1v1/t1) = (p2v2/t2)
To find the volume of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the given temperature from Celsius to Kelvin by adding 273.15 to it:
T = 140 ºC + 273.15 = 413.15 K
Next, we can rearrange the equation to solve for volume:
V = (nRT) / P
Now, let's substitute the given values into the equation:
n = 14 mol
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
Please note that the ideal gas constant has different values depending on the unit of pressure used. The value 0.0821 L·atm/(mol·K) is commonly used when the pressure is given in atmospheres, which is the case in this question. For other units of pressure, such as kilopascals (kPa), a different value should be used (e.g., 8.314 L·kPa/(mol·K)).
P = 233 kPa (kilopascals)
Now, we can substitute these values into the equation and solve for V:
V = (14 mol * 0.0821 L·atm/(mol·K) * 413.15 K) / 233 kPa
After canceling out the appropriate units and performing the calculation, the final volume can be obtained.
This calculation can further be simplified by converting the pressure into atmospheres if preferred, by using the conversion factor 1 atm = 101.325 kPa.