Calculate the molar mass of CH4 gas at STP when 5.46L Of the gas weights 4g
Check that wether it us done by P =DRT/M and the exact answer....
density of any gas is mass/volume.
at STP, that means molarmass/22.4liters
so since density will not change at STP..
molarmass/22.4L = 4.0g/5.46L or
molar mass= 22.4*4.0/5.46 grams
molar mass=16.1 grams looks very much like CH4 gas
To calculate the molar mass of CH4 gas, we need to use the ideal gas law. The ideal gas law equation is 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.
Since the problem states that we have CH4 gas at STP (standard temperature and pressure), we can assume that the temperature is 273.15K (0°C) and the pressure is 1 atm.
We are given the volume of the gas as 5.46L and the mass of the gas as 4g.
First, we need to convert the grams of CH4 to moles using the molar mass of CH4. To do this, we'll divide the mass of CH4 by its molar mass.
The molar mass of CH4 is calculated by adding up the atomic masses of each element in the compound.
For CH4, Carbon (C) has a molar mass of 12.01 g/mol, and Hydrogen (H) has a molar mass of 1.008 g/mol.
CH4 molar mass = 1 x (12.01 g/mol) + 4 x (1.008 g/mol) = 16.04 g/mol
Now we can calculate the number of moles using the given mass of 4g:
moles = mass / molar mass = 4g / 16.04 g/mol ≈ 0.249 mol
Using the ideal gas law equation PV = nRT, we need to find the value of n (number of moles), which is already calculated as 0.249 mol.
Since we know the temperature is 273.15K and the pressure is 1 atm, we can substitute the values:
PV = nRT
(1 atm) * (5.46 L) = (0.249 mol) * (0.0821 L·atm/mol·K) * (273.15K)
Simplifying the equation, we can solve for the molar mass (M):
M = (mass) / (moles)
M = 4g / 0.249 mol
M ≈ 16.10 g/mol
Therefore, the molar mass of CH4 gas at STP is approximately 16.10 g/mol.