Question

A balloon that can hold 35 L of air is inflated with 2.5 moles of gas at a pressure of 2.5

atmosphere. What is the temperature in °C of the balloon?

Answer 1

The temperature of the balloon is approximately 153.4°C.

Step-by-step explanation:

To find the temperature in Celsius of the balloon, we can use the ideal gas law.

Ideal Gas Law

`\boxed{\sf PV=nRT}`

where:

• P is the pressure measured in atmospheres (atm).
• V is the volume measured in liters (L).
• n is the number of moles.
• R is the ideal gas constant (0.08206 L atm mol⁻¹ K⁻¹).
• T is the temperature measured in kelvin (K).

Given values:

• P = 2.5 atm
• V = 35 L
• n = 2.5 mol
• R = 0.08206 L atm mol⁻¹ K⁻¹

Substitute the values into the formula and solve for T:

`\implies \sf 2.5 \cdot 35 = 2.5 \cdot 0.08206 \cdot T`

`\implies \sf T=(2.5 \cdot 35)/(2.5 \cdot 0.08206)`

`\implies \sf T=(87.5)/(0.20515)`

`\implies \sf T=426.5178...\;K`

As the temperature should be in Celsius, we need to convert from kelvin to Celsius by subtracting 273.15:

`\implies \sf T=426.5178...\;K-273.15=153.4^(\circ)C`

Therefore, the temperature of the balloon is approximately 153.4°C.