To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 1.00-L bulb, then filled it with the gas at 1.10 atm and 23.0 C and weighed it again. The difference in mass was 1.27 g . Identify the gas.
PV=nRT.
You know P, V, R and T. Calculate n = # mols of the gas.
Then you know mols = grams/molar mass.
You know mols and grams, calculate molar mass. Molar mass divided by 2 (since it is diatomic) = atomic mass. Look that up on the periodic table. Post your work if you get stuck.
C2H4
Rearrange the equation so it looks like n=PV/RT
First change 23C to Kelvin= 296 Kelvin
Plug in what you have:
n= (1.10atm)(1.00L)/(0.08206)(296)
n=0.045 that is the number of moles you have. But it doesn't tell you what type of element it is. So you need to find out the molar mass of the element.
take what the equation gives you for grams
1.27 and divide that by the number of moles you have
1.27grams/0.045mole = 28.22g/mol
But since it is a diatomic gas, that means you have to divide it by two to see the mass of each individual molecule.
28.22/2= 14.11
Look on the periodic table for the element with a mass of 14.11 it is Nitrogen.
So your answer would be N2
To identify the gas, we can use the ideal gas law which states:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = moles of gas
R = ideal gas constant (0.0821 L*atm/mol*K)
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 23.0 + 273.15
T(K) = 296.15 K
Next, let's calculate the number of moles of gas using the ideal gas law:
n = (PV) / (RT)
Rearranging the equation, we have:
n = (P * V) / (R * T)
n = (1.10 atm) * (1.00 L) / (0.0821 L*atm/mol*K * 296.15 K)
n ≈ 0.0415 mol
Now that we have the number of moles, we can calculate the molar mass of the gas by dividing the difference in mass by the number of moles:
Molar mass = (Difference in mass) / (Number of moles)
Molar mass = 1.27 g / 0.0415 mol
Molar mass ≈ 30.6 g/mol
From the calculated molar mass, we can determine the identity of the gas. In this case, the molar mass is approximately 30.6 g/mol. Since the gas is diatomic, the molar mass should be close to the atomic mass of one of the elements. In this case, the closest match is chlorine (Cl) which has an atomic mass of approximately 35.5 g/mol.
Therefore, based on the given information, it can be concluded that the diatomic gas is chlorine gas (Cl2).