Calculating ΔS for Mixing H20 and D20 Solutions

[ebunny91]

Homework Statement

For both H20 and D20:
Cp = 75.5 J/mole-k for the liquid Cp = 37.8 J/mole-k for the solid ΔHfus=6.01 kJ/mole.

Liquid H20 and D20 form an ideal solution.

a) One mole of liquid H20 at 10 C is mixed with four moles of LIQUID D20 at 0 C in an insulated container.
Determine ΔS.

b) One mole of liquid H20 at 10 C is mixed with four moles of SOLID D20 at 0 C in an insulated container.
Determine ΔS.

Homework Equations

ΔSmixing = -R(nX1lnX1 + nX2lnX2)

The Attempt at a Solution

I found
ΔSmixing = -R(nX1lnX1 + nX2lnX2) = -8.324[(1mol)(1/5)ln(1/5) + (4mol)(4/5)ln(4/5)] = 8.612 j/mol-k

I don't really understand the question. Can someone explain some of he concepts I need to know or direct me to somewhere where it sums it up?

What are the steps to solving this? What do I have to think about? (Like...I know X, so I get Y because of Z)

 

[nate808]

Hi there! Let's break down the problem and go through the steps to solve it.

Step 1: Understand the problem
The problem is asking you to calculate the change in entropy (ΔS) when mixing different quantities of liquid H20 and D20 at different temperatures. The given information includes the specific heat capacity (Cp) and the enthalpy of fusion (ΔHfus) for both substances.

Step 2: Identify the relevant equations
The equation you need to use is ΔSmixing = -R(nX1lnX1 + nX2lnX2). This equation relates the change in entropy to the number of moles (n) and the mole fraction (X) of each substance in the mixture. R is the gas constant, which has a value of 8.314 J/mol-k.

Step 3: Determine the number of moles and mole fractions
a) In the first scenario, we have 1 mole of liquid H20 and 4 moles of liquid D20. The total number of moles is 5. The mole fraction of H20 is 1/5 = 0.2, and the mole fraction of D20 is 4/5 = 0.8.
b) In the second scenario, we have 1 mole of liquid H20 and 4 moles of solid D20. The total number of moles is still 5. However, since the D20 is now in its solid form, we need to consider its enthalpy of fusion. This means that we need to take into account the energy required to convert the solid D20 into liquid D20. This will affect the mole fraction of D20 in the mixture.

Step 4: Calculate the change in entropy
a) Plugging in the values from part a, we get ΔSmixing = -8.314[(1mol)(0.2)ln(0.2) + (4mol)(0.8)ln(0.8)] = 8.612 J/mol-k.
b) For part b, we need to consider the change in enthalpy when converting the solid D20 into liquid D20. This can be calculated using the enthalpy of fusion (ΔHfus) and the number of moles of D20. The enthalpy change for this process is ΔH = (4mol)(6.