A 0.286g sample of carbon dioxide, CO2, has a volume of 585mL and a pressure of 495mmHg . What is the temperature, in kelvins and degrees Celsius, of the gas?
Use PV = nRT and solve for T which will be in kelvin. Then
kelvin = 273 + C
n = number of mols = grams/molar mass
How would i use the grams in this equation though?
That's the line I wrote for
n = grams/molar mass
You must have n for PV = nRT
n = number mols CO2 and that is grams CO2/molar mass CO2
n = 0.286/44 = ?
To determine the temperature of the gas, 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 liters),
n is the number of moles of the gas,
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
T is the temperature of the gas (in Kelvin).
First, let's convert the given values to the appropriate units.
Given:
Mass of CO2 (m) = 0.286g
Volume of CO2 (V) = 585mL = 0.585L
Pressure of CO2 (P) = 495mmHg
R = 0.0821 L·atm/(mol·K)
First, we need to calculate the number of moles (n) of CO2 present in the sample.
To find the number of moles, we can use the formula:
n = (mass of CO2) / (molar mass of CO2)
The molar mass of CO2 is calculated by adding up the atomic masses of carbon and oxygen:
Molar mass of C = 12.01 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of CO2 = (12.01 g/mol) + (16.00 g/mol) + (16.00 g/mol) = 44.01 g/mol
Now, we can calculate the number of moles:
n = (0.286g) / (44.01 g/mol) = 0.0065 mol
Next, rearrange the ideal gas law equation to solve for temperature (T):
T = (PV) / (nR)
Now plug in the known values:
T = (495 mmHg) * (0.585 L) / (0.0065 mol * 0.0821 L·atm/(mol·K))
First, we need to convert the pressure from mmHg to atm:
1 atm = 760 mmHg
So, (495 mmHg) / (760 mmHg/atm) = 0.651 atm
Now, substitute the values into the equation:
T = (0.651 atm) * (0.585 L) / (0.0065 mol * 0.0821 L·atm/(mol·K))
T = 524.95 K
To convert Kelvin to degrees Celsius, use the formula:
T(°C) = T(K) - 273.15
T(°C) = 524.95 K - 273.15
T(°C) = 251.80 °C
Therefore, the temperature of the gas is 524.95 Kelvin or 251.80 degrees Celsius.