Ideal Gas Equation

Question

Calculate the temperature at which 1.00 mole of oxygen at 0°C and 760 mm Hg would triple in volume at a pressure of 1520 mm Hg.

Answer 1

Hey Ivan,

Often, mistakes on these problems come down to units. Typically, we use SI units, making R = 8.3145 J/mol/K. This means that you should put your temperatures in Kelvin and your pressure values in Pascals.

Now you can solve the ideal gas law for V: V = nRT/P.

1. The straightforward, "plug 'n chug" way would be to calculate V with the initial conditions, triple that number, then use that new Volume along with the new pressure (still with n = 1.00 mol) to find your new Temperature.
2. Another way would be thinking of this as a "factor of change" type problem, which lets us minimize calculations. With this method, we replace each variable in the equation with the multiplier that it undergoes.
3. So V would be replaced with a [3], because it triples. P would be replaced with a [2], because it doubles. n and R can be replaced with a [1], because they do not change.
4. This leaves us with: [3] = [1] * [1] * [??] / [2], where "??" represents the multiplier for temperature.
5. This gives us [??] = [6], meaning that the new temperature is 6 times higher than the original (in Kelvin).