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?

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thomasdecabooter thomasdecabooter · Answer 1 · 2019-10-27T02:40:45+02:00

Answer:

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