We consider an ideal gas of molar mass M = 16 g/mol at +10oC. What is the pressure of the gas if its density is 1.16 kg/m3 ?
To find the pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
First, let's find the volume using the given density. Density is defined as mass divided by volume, so the volume can be determined by dividing the mass of the gas by its density:
volume = mass / density
Given that the molar mass of the gas (M) is 16 g/mol, the mass can be calculated using the molar mass and the number of moles:
mass = number of moles * molar mass
Since the number of moles is not provided in the given information, we need to find it using the ideal gas equation:
PV = nRT
Rearranging the equation, we get:
n = PV / RT
Now we have all the necessary values to calculate the pressure. Let's substitute the known values into the equations:
1. Calculate the mass:
mass = number of moles * molar mass
mass = n * M
2. Calculate the volume:
volume = mass / density
3. Calculate the number of moles:
n = PV / RT
4. Finally, calculate the pressure:
P = (nRT) / V
Substitute the calculated values into the pressure equation:
P = [(PV / RT) * RT] / (mass / density)
P = (PV * density) / molar mass
Now, plug in the given values for temperature, density, and molar mass into the pressure equation and solve for P.