The gaseous product of a reaction is collected in a 25 L container at 27 degrees Celsius. The pressure in a container is 300 kPa and the gas has a mass of 96 g. What is the formula mass of the gas?
PV=nRT= mass/molmass * RT
solve for molemass
To determine the formula mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in Pa)
V = Volume (in m^3)
n = Number of moles
R = Gas constant (8.314 J/(mol·K))
T = Temperature (in Kelvin)
First, we need to convert the given values to the appropriate units. Since the pressure is given in kPa, we need to convert it to Pa:
300 kPa = 300,000 Pa
The volume is given as 25 L, so we need to convert it to m^3:
25 L = 0.025 m^3
The given temperature is 27 degrees Celsius, so we need to convert it to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 27 + 273.15
T(K) = 300.15 K
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (300,000 Pa) * (0.025 m^3) / [(8.314 J/(mol·K)) * (300.15 K)]
Now, we can simplify this equation to get the number of moles (n). Next, we can convert the given mass of 96 g to moles using the formula mass:
n = mass / formula mass
Rearranging this equation, we can solve for the formula mass:
formula mass = mass / n
Substituting the given values, we have:
formula mass = 96 g / n
We substitute the value of n from the ideal gas law equation to obtain the formula mass. However, the value of n depends on the given gas and cannot be determined without additional information such as the identity of the gas.
To find the formula mass of the gas, we need to 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 Kelvin.
First, we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature (TK) is calculated by adding 273.15 to the Celsius temperature (TC). So, 27 degrees Celsius would be 27 + 273.15 = 300.15 K.
Next, we can rearrange the Ideal Gas Law equation to solve for the number of moles (n) using the equation: n = PV / RT.
We have the pressure (P) as 300 kPa, the volume (V) as 25 L, and the temperature (T) as 300.15 K. The ideal gas constant (R) is typically given as 0.0821 L·atm/(mol·K).
Now, let's plug in these values into the equation:
n = (300 kPa) * (25 L) / (0.0821 L·atm/(mol·K) * 300.15 K).
Note that we need to convert the pressure from kPa to atm by dividing by 101.325 (1 atm = 101.325 kPa).
n = (300 kPa / 101.325) * (25 L) / (0.0821 L·atm/(mol·K) * 300.15 K).
Simplifying further:
n ≈ 7.41 mol.
Now, to find the formula mass, we divide the mass of the gas (96 g) by the number of moles. Therefore, the formula mass is 96 g / 7.41 mol ≈ 12.97 g/mol. So, the formula mass of the gas is approximately 12.97 g/mol.