A large flexible balloon contains 3.5moles of pure nitrogen gas at 1.0atm pressure and 0∘C. What is the volume of the balloon?

Answer 1

The Ideal Gas Law states:

PV=nRT

where P is the pressure, V is the volume, n is the number of moles, R is the Ideal Gas Constant, and T is the temperature.

Solving for V, we get:

V = nRT/P

BUT, we need to be careful about the units. We can look up (Google) the value of R for various units and get R = 0.08205746 L•atm/(K•mol) which uses pressure in atmospheres (like we have) but notice it requires temperature in K. So K = 273.15 + °C so in this case, 0 °C = 273.15 K. Also notice that using this value of R will give us an answer of volume in liters (L)

So, plugging in those value into the equation gives:

V = nRT/P

V = (3.5)(0.08205746)(273.15)/(1.0) = 78 L

In reality, since the number of sig figs in 0 °C is just 1, the answer should actually be 80 L.