Ten fully worked problems spanning Boyle's, Charles', Gay-Lussac's, and Avogadro's Laws, the
combined and ideal gas laws, STP, and an adiabatic process, each with every step shown.
Want to check your own numbers instead? Use the interactive combined gas law calculator on the
homepage, or jump to the specific law calculator linked under each example below.
How many moles of gas are in a 10.0 L cylinder at 2.50 atm and 27°C?
Given: P = 2.50 atm, V = 10.0 L, T = 27°C. Find: n.Convert to Kelvin: T = 300.15 K. Convert R to match units: R = 0.082057 L·atm/(mol·K)Ideal gas law: PV = nRT → n = PV / (RT)n = (2.50 × 10.0) / (0.082057 × 300.15)n ≈ 1.02 mol
What pressure does 0.500 mol of gas exert in a 5.00 L container at 350 K?
Given: n = 0.500 mol, V = 5.00 L, T = 350 K. Find: P.Use R = 0.082057 L·atm/(mol·K) since volume is in liters.Ideal gas law: PV = nRT → P = nRT / VP = (0.500 × 0.082057 × 350) / 5.00P ≈ 2.87 atm
How do I know which gas law to use for a word problem?
Check what's changing and what's fixed. If only pressure and volume change (temperature fixed), use Boyle's Law. If only volume and temperature change (pressure fixed), use Charles' Law. If only pressure and temperature change (volume fixed), use Gay-Lussac's Law. If all three change, use the combined gas law. If you need to find the amount of gas (moles), use the ideal gas law.
Do I need to convert units before solving these examples?
You need consistent units within each side of the equation, and temperature must always be in Kelvin. Each example below shows any necessary conversions as an explicit step, so you can see exactly when and why they're needed.
Can I check my own homework answer against these examples?
Yes: work through a similar problem using the same method shown here, then verify your numeric answer using the combined gas law calculator on the homepage or the specific law calculator linked from each example.
Why do some examples give answers in scientific notation?
Very small or very large numbers (common in moles, or extreme pressures) are easiest to read in scientific notation. Every calculator on this site displays results this way automatically once a number falls outside a normal everyday range.
Why do some of these examples round to a different number of decimal places than others?
The number of significant figures shown generally matches the precision of the numbers given in the problem, a problem with values given to three significant figures (like 1.20 atm) is answered to a similar precision, rather than displaying a long string of digits that would imply more precision than the original data actually supports.