Question

The change in entropy of the gas when 4g of nitrogen is allowed to expand is othermally from 500 cm³ to 750 cm³ at 300k exceeds 0.9 j/k, True or false

Answer 1

The change in entropy of a gas during an isothermal expansion can be calculated using the formula: ΔS = nR ln(Vf/Vi). In this case, the calculated change in entropy exceeds 0.9 J/K, so the statement is true.

Step-by-step explanation:

The change in entropy of a gas during an isothermal expansion can be calculated using the formula:

ΔS = nR ln(Vf/Vi)

Where ΔS is the change in entropy, n is the number of moles of gas, R is the gas constant, Vf is the final volume, and Vi is the initial volume.

In this case, we are given the initial and final volumes and the number of moles of nitrogen gas (which can be calculated using the molar mass of nitrogen and the mass given). Plugging in these values, we can compare the calculated change in entropy to the value given in the question to determine if it exceeds 0.9 J/K.

Example Calculation:

n = mass / molar mass = 4g / 28 g/mol = 0.143 mol

ΔS = 0.143 mol * 8.314 J/(mol*K) * ln(750 cm³ / 500 cm³) ≈ 1.96 J/K

Since the calculated change in entropy (1.96 J/K) is greater than 0.9 J/K, the statement is true.

Answer 2

The change in entropy of the gas when 4g of nitrogen expands isothermally from 500 cm³ to 750 cm³ at 300K is calculated to be 0.489 J/K, which is less than 0.9 J/K. Therefore, the statement is false.

Step-by-step explanation:

The question is about determining whether the change in entropy of the gas when 4g of nitrogen is allowed to isothermally expand from 500 cm³ to 750 cm³ at 300K exceeds 0.9 J/K. To find this, we can use the formula for the entropy change of an ideal gas during isothermal expansion, which is ΔS = nRln(Vf/Vi), where n is the number of moles, R is the gas constant (8.314 J/mol·K), Vf is the final volume, and Vi is the initial volume.

First, we calculate the number of moles of nitrogen using its molar mass (N2 = 28 g/mol): n = mass/molar mass = 4g/(28g/mol) = 0.143 mol. Then we use the entropy change formula: ΔS = 0.143 mol × 8.314 J/mol·K × ln(750/500) = 0.143 mol × 8.314 J/mol·K × ln(1.5) = 0.143 mol × 8.314 J/mol·K × 0.4055 = 0.489 J/K.

Since 0.489 J/K is less than 0.9 J/K, the statement that the change in entropy exceeds 0.9 J/K is false.