Question

A helium-filled balloon at 310.0 K and 1 atm, contains 0.05 g He, and has a volume of 1.28 L. It is placed in a freezer (T = 250.0 K), and its volume decreases to 0.94 L. Find ΔE for the gas (in joules). (Cp of He = 20.8 J/mol K.)

Answer 1

The change in internal energy for the helium gas is -15.60 J.

Step-by-step explanation:

To calculate the change in internal energy, we can use the equation: ΔE = nCpΔT, where n is the number of moles, Cp is the molar heat capacity at constant pressure, and ΔT is the change in temperature. In this case, we need to find the change in internal energy, so we can use the final and initial temperatures. Let's start by finding the number of moles of helium using the molar mass.

Given:

• T1 = 310.0 K
• T2 = 250.0 K
• V1 = 1.28 L
• V2 = 0.94 L
• m = 0.05 g
• Cp = 20.8 J/mol K

First, convert the mass of helium to moles:

n = m / M, where M is the molar mass of helium (4.0026 g/mol).

Substituting the values, we get:

n = 0.05 g / 4.0026 g/mol = 0.01249 mol

Next, calculate the change in temperature:

ΔT = T2 - T1 = 250.0 K - 310.0 K = -60.0 K

Now, we can calculate the change in internal energy:

ΔE = nCpΔT = 0.01249 mol x 20.8 J/mol K x -60.0 K = -15.60 J

The change in internal energy for the gas is -15.60 J. Since the quantity is negative, it means that the internal energy of the gas has decreased.