2.05 g of an unknown gas at 45 °C and 1.00 atm is stored in a 1.15-L flask.
What is the density of the gas?
I would use (V1/T1) = (V2/T2). You want to correct T = 45 C to (convert to kelvin of course) to T at zero and calculate the new V2 at those conditions. Then density = grams/V2 (in L) to give density in g/L.
T1 is 288K but what is T2?
T2 is T at standard conditions. Isn't that 273 K. So you're correct volume from 288 K to 273 K.
(Note: You know the density at 45 C; it's 2.05g/1.15 l)
To find the density of the gas, we need to use the ideal gas law equation, which relates the pressure, volume, temperature, and molar mass of the gas.
The ideal gas law equation is:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal Gas Constant (0.0821 L·atm/(mol·K))
T = Temperature (in Kelvin)
To find the density, we need the mass of the gas and its volume. Given that the mass of the gas is 2.05 g and the volume is 1.15 L, we can proceed as follows:
Step 1: Convert the temperature from Celsius to Kelvin
To convert Celsius to Kelvin, we need to add 273.15 to the temperature in Celsius. In this case, the temperature is 45 °C, so the corresponding Kelvin temperature would be:
T = 45 °C + 273.15 = 318.15 K
Step 2: Convert the mass to moles
We can use the molar mass of the gas to convert the given mass to moles. Since the molar mass of the gas is unknown, we cannot directly calculate the number of moles, so we will use an additional step.
Step 2.1: Calculate the molar mass of the gas
To calculate the molar mass, we need to know the identity of the gas. Once we know the identity, we can determine its molar mass from the periodic table.
Step 3: Calculate the number of moles
Using the molar mass of the gas obtained in the previous step, we can calculate the number of moles using the formula:
n = mass (in grams) / molar mass (in g/mol)
Step 4: Use the ideal gas law to find the density
Now that we have the number of moles (n), the pressure (P), the volume (V), and the temperature (T) in Kelvin, we can use the ideal gas law equation to find the density of the gas.
To do this, we rearrange the equation to isolate the density (d):
d = (mass of the gas / volume of the gas)
Substituting the known values, we get:
d = (molar mass * n) / V
By plugging in the calculated values for the molar mass, the number of moles, and the volume, we can find the density of the gas.