What is the density of CH4 gas at 32.7 degree celsius and 109kPa? The molar mass of CH4 is 16.042g/mol.
you know PV=kT
solve for V, then use
density = mass/volume
30
To find the density of CH4 gas at a specific temperature and pressure, you need to use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
In this case, we are given the temperature in Celsius, so we need to convert it to Kelvin.
T(K) = T(°C) + 273.15
T(K) = 32.7 + 273.15
T(K) = 305.85 K
Next, we can rearrange the ideal gas law equation to solve for density:
P = nRT/V
Since we are given the molar mass of CH4, we can use it to calculate the number of moles (n) using the formula:
n = molar mass / mass
Where:
molar mass = 16.042 g/mol
mass = mass of CH4 gas
Now let's substitute the given values into the equation to calculate the density:
P = 109 kPa
T = 305.85 K
R = 0.0821 L·atm/(mol·K)
First, we need to convert the pressure from kPa to atm:
1 atm = 101.325 kPa
109 kPa = 109 / 101.325 atm
Now, let's solve for the number of moles (n):
n = molar mass / mass
We don't have the mass of CH4 gas, but we can use the density formula to find it:
density = mass / volume
Rearranging the formula, we can find the mass:
mass = density * volume
Since we are calculating for density, we need to isolate it:
density = mass / volume
Substituting this equation into n = molar mass / mass, we can solve for n:
n = molar mass / (density * volume)
Now we have all the values needed to calculate n:
n = 16.042 g/mol / (density * volume)
Finally, substitute all the values, solve for n, and then substitute the values of n, P, T, and R into the ideal gas law equation:
P = (16.042 g/mol / (density * volume)) * (0.0821 L·atm/(mol·K)) * 305.85 K
Now solve the equation for density.
Please note that the provided solution is a general approach to solve the problem. Some specific details may be required depending on the context or assumptions made.