Calculating the density of a gas at STP
Confused about how to calculate the density of a gas at STP? Follow these step by step instructions.
Helpful reference for checking your findings of molecular weight and molar mass: http://www.lenntech.com/calculators/molecular/molecular-weight-calculator.htm
[Note: I do not 100% guarantee that any of my work is correct- it's just done to the best of my abilities- so please double check your answers if following my method to solve a similar problem]
*Remember significant figures! I'm not the best at sig. fig., but hopefully all my work is accurate.*
Problem: Calculate the density of CH4 gas at STP.
How to solve the problem: Density is mass over volume. (D = M/V), this is what we need to find.
Information you will need:
Molecular weight of CH4 = 16.05 g/mol
STP = Pressure (P) = 1 atm (unit of pressure) and Temperature (T) à 273 K (unit of temperature)
Use the ideal gas law. PV = nRT
n = mass/ mw (molecular weight- “The molecular weight is essentially the same thing as the molar mass except that, as the name implies, it refers to molecules rather than just elements. The molar mass and molecular weight is typically given in units of grams per mole.” - Answers.com)
n = unit of mass
V = unit of volume
PV = (mass/mw) RT
Steps:
Re-arrange the ideal gas law equation, so that you get M/V (which is density).
Mass/V = mw (molecular weight) x P/ RT
Mass/V = (16.05 g/mol) x 1 atm / [0.08206 (L)(atm)/ (mol)(K)] (273 degrees K)
Because of the gas law constant, atm (unit of pressure), K (unit of temperature) and mol (numerical unit) cancel out, and we are left with units of grams per L (unit of volume), which is what we want. Thus, our answer will be in units of g/L.
Plug the equation into your scientific calculator.
I got 7.16 x 10^-1 g/L
Helpful reference for checking your findings of molecular weight and molar mass: http://www.lenntech.com/calculators/molecular/molecular-weight-calculator.htm
[Note: I do not 100% guarantee that any of my work is correct- it's just done to the best of my abilities- so please double check your answers if following my method to solve a similar problem]
*Remember significant figures! I'm not the best at sig. fig., but hopefully all my work is accurate.*
Problem: Calculate the density of CH4 gas at STP.
How to solve the problem: Density is mass over volume. (D = M/V), this is what we need to find.
Information you will need:
Molecular weight of CH4 = 16.05 g/mol
STP = Pressure (P) = 1 atm (unit of pressure) and Temperature (T) à 273 K (unit of temperature)
Use the ideal gas law. PV = nRT
n = mass/ mw (molecular weight- “The molecular weight is essentially the same thing as the molar mass except that, as the name implies, it refers to molecules rather than just elements. The molar mass and molecular weight is typically given in units of grams per mole.” - Answers.com)
n = unit of mass
V = unit of volume
PV = (mass/mw) RT
Steps:
Re-arrange the ideal gas law equation, so that you get M/V (which is density).
Mass/V = mw (molecular weight) x P/ RT
Mass/V = (16.05 g/mol) x 1 atm / [0.08206 (L)(atm)/ (mol)(K)] (273 degrees K)
Because of the gas law constant, atm (unit of pressure), K (unit of temperature) and mol (numerical unit) cancel out, and we are left with units of grams per L (unit of volume), which is what we want. Thus, our answer will be in units of g/L.
Plug the equation into your scientific calculator.
I got 7.16 x 10^-1 g/L