A 0.200 g sample of carbon dioxide, CO2, has a volume of 525 mL and a pressure of 473 mmHg .
What is the temperature of the gas in kelvins?
To calculate the temperature of the gas in kelvins, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P is the pressure,
V is the volume,
n is the number of moles,
R is the ideal gas constant, and
T is the temperature in kelvins.
First, we need to calculate the number of moles of CO2 using its molar mass.
The molar mass of CO2 is:
12.01 g/mol for carbon (C) +
2(16.00 g/mol) for oxygen (O).
So, the molar mass of CO2 is 44.01 g/mol.
Given that the mass of the sample is 0.200 g, we can calculate the number of moles using the formula:
moles = mass / molar mass
moles = 0.200 g / 44.01 g/mol.
moles = 0.004545 mol.
Now, we can rearrange the Ideal Gas Law equation to solve for temperature:
T = (PV) / (nR).
First, let's convert the pressure from mmHg to atm:
1 atm = 760 mmHg.
So, the pressure is 473 mmHg / 760 mmHg/atm = 0.622 atm.
Now, we can substitute the values into the equation:
T = (0.622 atm) x (525 mL) / (0.004545 mol) x (0.08206 L·atm/(mol·K)).
Simplifying the equation:
T = (0.622 atm) x (0.525 L) / (0.004545 mol) x (0.08206 L·atm/(mol·K)).
Calculating the temperature:
T = 498.69 K.
Therefore, the temperature of the gas in kelvins is 498.69 K.
To determine the temperature of the gas in kelvins, we can use the ideal gas law, which states:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = amount of substance (in moles)
R = ideal gas constant
T = temperature in kelvins
We have the values of pressure (473 mmHg) and volume (525 mL), but we need to find the amount of substance (n) to calculate the temperature.
To find the amount of substance, we can use the formula:
n = m/M
Where:
m = mass of the substance
M = molar mass of the substance
Given that the sample has a mass of 0.200 g and it's carbon dioxide (CO2), which has a molar mass of 44.01 g/mol, we can substitute these values to find n.
n = 0.200 g / 44.01 g/mol
n ≈ 0.00454 mol
Now that we know the amount of substance (n), we can rearrange the ideal gas law equation to solve for temperature (T):
T = PV / (nR)
Substituting the known values, we get:
T = (473 mmHg * 525 mL) / (0.00454 mol * R)
Note: We need to convert millimeters of mercury (mmHg) to atmospheres (atm) and convert milliliters (mL) to liters (L) to ensure consistent units.
1 atm = 760 mmHg
1 L = 1000 mL
Converting the units, we have:
T = ((473 mmHg / 760 mmHg/atm) * (525 mL / 1000 mL/L)) / (0.00454 mol * R)
Simplifying further:
T = (0.62 atm * 0.525 L) / (0.00454 mol * R)
Now, we just need to substitute the value of the ideal gas constant, R, which is 0.0821 L·atm/(K·mol), to calculate the temperature.
T = (0.62 atm * 0.525 L) / (0.00454 mol * 0.0821 L·atm/(K·mol))
Simplifying the equation:
T = (0.3255 atm·L) / (0.0373309 atm·L/(K·mol))
T ≈ 8.721 K
Therefore, the temperature of the gas is approximately 8.721 Kelvin.