A 1.26 g sample of He gas has a pressure of 0.123 atm and a volume of 32.6 L. What is the temperature of the sample, in °C?
-118*C
To find the temperature of the sample, we can use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure of the gas (in atm),
- V is the volume of the gas (in L),
- n is the number of moles of gas,
- R is the ideal gas constant (0.0821 L·atm/mol·K),
- T is the temperature of the gas (in Kelvin).
First, we need to convert the given pressure from atm to Pa (Pascal):
1 atm = 101325 Pa
So, the pressure in Pa can be calculated as:
P_pa = P * 101325
Now, let's rearrange the ideal gas law to solve for temperature:
T = (PV) / (nR)
We need to determine the number of moles of gas (n) from the given sample mass (m) and the molar mass of helium (MH):
n = m / MH
The molar mass of helium is approximately 4.00 g/mol.
Now, we can substitute the given values into the equation and calculate the temperature:
1. Convert the mass of the sample from grams to moles:
m = 1.26 g
MH = 4.00 g/mol
n = m / MH
2. Calculate the molar amount of gas (n):
n = 1.26 g / 4.00 g/mol
3. Convert the pressure from atm to Pa:
P = 0.123 atm
P_pa = 0.123 atm * 101325 Pa/atm
4. Calculate the temperature using the ideal gas law equation:
T = (P_pa * V) / (n * R)
Substituting the given values, we can now calculate the temperature.