A sample of neon gas is held in a rigid 2.284L container with a pressure of 1.036 atm at 24.3°C. 4.093g of an unknown cold gas is added to the container. The temperature drops to 20.3°C, but the pressure rises to 1.960atm. What is the molar mass of the added gas?
i came up with a MM of 42.2 but i do not feel that it is the correct answer how would i solve this problem
i figured it out 11.5 g
To determine the molar mass of the added gas, 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
T is the temperature
First, let's calculate the initial number of moles of neon gas using the given information:
Pressure of neon gas (P1) = 1.036 atm
Volume of the container (V1) = 2.284 L
Temperature of the neon gas (T1) = 24.3°C = (24.3 + 273.15) K (converted to Kelvin using the Kelvin conversion: K = °C + 273.15)
Ideal gas constant (R) = 0.0821 L·atm/(K·mol) (given)
Rearranging the equation for the initial state (State 1):
PV = nRT
n = (PV) / (RT)
n1 = ((1.036 atm) * (2.284 L)) / ((0.0821 L·atm/(K·mol)) * (24.3 + 273.15) K)
Next, let's calculate the final number of moles of gas in the container after the unknown cold gas is added:
Pressure of the final gas (P2) = 1.960 atm
Volume of the container (V2) = 2.284 L
Temperature of the final gas (T2) = 20.3°C = (20.3 + 273.15) K (converted to Kelvin)
Using the same formula as before:
n2 = ((1.960 atm) * (2.284 L)) / ((0.0821 L·atm/(K·mol)) * (20.3 + 273.15) K)
The change in the number of moles (Δn) is the difference between n2 and n1:
Δn = n2 - n1
Now that we have the change in moles, we can calculate the molar mass of the added gas:
Molar mass (M) = (mass of the added gas) / (Δn)
Given that the mass of the added gas is 4.093 g, we can now substitute the values into the equation:
M = (4.093 g) / (Δn)
Substitute the calculated value of Δn into the equation to find the molar mass of the added gas.