Question

I place a balloon in my fridge that initially has a pressure of 1.02 atm and a temperature of 11.2 0C. What will be the pressure of the balloon be (in atm) when it is fully cooled to 4.000 C by my refrigerator? Round your answer to correct sig figs. Do not include units in your answer.

Answer 1

The pressure of the balloon when it is fully cooled to 4.000°C is 0.994 atm (rounded to 3 significant figures).

Step-by-step explanation:

To solve this problem, we can use the Ideal Gas Law:

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 in Kelvin.

First, we need to convert the initial temperature from Celsius to Kelvin:

T1 = 11.2°C + 273.15 = 284.35 K

Next, we can use the given pressure, temperature, and the Ideal Gas Law to find the initial volume of the balloon:

V1 = nRT1/P1

Now, we need to find the final pressure of the balloon when it is cooled to 4.000°C. We can assume that the volume of the balloon remains constant throughout the cooling process since it is sealed.

T2 = 4.000°C + 273.15 = 277.15 K

P2 = nRT2/V1

Since the number of moles and volume of the balloon do not change, we can rewrite the above equation as:

P2/P1 = T2/T1

Solving for P2, we get:

P2 = P1(T2/T1) = 1.02 atm x (277.15 K/284.35 K) = 0.994 atm

Therefore, the pressure of the balloon when it is fully cooled to 4.000°C is 0.994 atm (rounded to 3 significant figures).