a sample of methane gas of mass 25g at 250k and 18.8atm expands isothermally until its pressure is 2.5atm. calculate the change in entropy.

Use dS = nR*ln(P1/P2)

26.144

To calculate the change in entropy during an isothermal expansion, you can use the formula:

ΔS = nR ln(V2/V1)

Where:
ΔS = Change in entropy
n = Number of moles of gas
R = Ideal gas constant (8.314 J/(mol·K))
V1 = Initial volume of gas
V2 = Final volume of gas

First, let's calculate the number of moles of methane gas (CH4) using its mass and molar mass:

Molar mass of CH4 = 12.01 g/mol (C) + 4(1.01 g/mol) (4H) = 16.05 g/mol

Number of moles (n) = mass/molar mass = 25g/16.05 g/mol ≈ 1.557 mol

Since the process is isothermal, the temperature remains constant. Therefore, we don't need to consider temperature in our calculations.

Next, we need to find the initial and final volumes of the gas. We can use the ideal gas law equation to do this:

PV = nRT

Where:
P = Pressure
V = Volume
R = Ideal gas constant (8.314 J/(mol·K))
T = Temperature

Initial volume:
P1V1 = nRT1
V1 = (nRT1) / P1 = (1.557 mol * 8.314 J/(mol·K) * 250 K) / 18.8 atm ≈ 256.89 L (converting atm to L using 1 atm = 22.4 L)

Final volume:
P2V2 = nRT2
V2 = (nRT2) / P2 = (1.557 mol * 8.314 J/(mol·K) * 250 K) / 2.5 atm ≈ 627.62 L

Now, we can plug in the values into the equation for entropy change:

ΔS = nR ln(V2/V1)
ΔS = 1.557 mol * 8.314 J/(mol·K) * ln(627.62 L/256.89 L)

Calculating this value should give you the change in entropy (ΔS) during the isothermal expansion of the methane gas.

To calculate the change in entropy for an isothermal process, we can use the equation:

ΔS = nRln(V₁/V₂)

Where:
ΔS is the change in entropy
n is the number of moles of gas
R is the ideal gas constant (8.314 J/(mol·K))
V₁ is the initial volume of the gas
V₂ is the final volume of the gas

To find the number of moles of methane gas, we can use its molar mass, which is 16.04 g/mol. So,

number of moles (n) = mass / molar mass

Given:
Mass of methane gas = 25 g
Molar mass of methane gas = 16.04 g/mol
Initial pressure (P₁) = 18.8 atm
Final pressure (P₂) = 2.5 atm
Temperature (T) = 250 K

First, let's find the initial volume (V₁) using the ideal gas law equation:

PV = nRT

Rearranging the equation gives:

V₁ = (nRT) / P₁

Substituting the given values:

V₁ = (n × 8.314 J/(mol·K) × 250 K) / 18.8 atm

Now, let's find the final volume (V₂) using the same equation:

V₂ = (n × 8.314 J/(mol·K) × 250 K) / 2.5 atm

Finally, substitute the values of V₁, V₂, and n into the formula for entropy change:

ΔS = nRln(V₁/V₂)

Calculate the values and substitute them into the formula to find the change in entropy.