A hot-air balloon is filled with air to a volume of 4.00 3 103 m3 at 745 torr and 218C. The air in the balloon is then heated to 628C, causing the balloon to expand to a volume of 4.20 3 103 m3. What is the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon?

The ratio of number of moles is 0.572

Explanation:

Step 1: Given data

A hot-air balloon has a volume of 4*10³ m³

The pressure is 745 torr = 0.98 atm

The temperature in the ballon is 218 °C = 491.15 Kelvin

The temperature is raised to 628 °C (901.15 Kelvin) which makes to volume expand to 4.20 * 10³ m³

Step 2: Calculate the ratio of number of moles

In this situation we will use the ideal gas law

PV = nRT

We can rearrange this formula to

P1V1 / (n1T1) = P2V2 / (n2T2)

To find the ratio of the number of moles we should rearrange this into:

(n2 / n1) = (P2 / P1) * (V2 / V1) * (T1 / T2)

The P is constant so P1 = P2

This gives us:

(n2 / n1) = (V2 / V1) x (T1 / T2)

(n2 / n1) = (4.20 * 10³L / 4.00*10³L) * (491.15K / 901.15K) =

The ratio of number of moles is 0.572