How Do Phase Changes Affect Energy Calculations in Ethanol?

[nobb]

Hey...I am having a little problem with my homework. Here are the two questions:

1. 6.66g of ethanol gas at 78.3 degress celsius (boiling pt) was bubbles into 60g of liquid ethanol at 12.3 degrees celsius, heating it to 52.3 degrees. Specific heat for ethanol (l) is 2.6 g/(g degrees celsius). Use this data to calculate the molar heat vaporization for ethanol.

2. 30g of ethanol(l) (c=2.6 j/(g degrees celsius)) at 50 degrees has an ice cube at 0 degrees placed in it and the temperature drops to 14.5 degrees. Calculate the mass of the ice cube.


Could someone please explain to me how these questions are done? Thanks.

 

[member 553083]

For the first question, you need to use the equation q = m × c × ΔT, where q is the amount of heat energy, m is the mass of the ethanol, c is its specific heat, and ΔT is the change in temperature. Using this, you can calculate the amount of heat energy absorbed by the liquid ethanol. You will then use the molar heat of vaporization equation, q = ΔHvap, where ΔHvap is the molar heat of vaporization, to solve for the molar heat of vaporization. For the second question, you will use the equation q = m × c × ΔT, where q is the amount of heat energy, m is the mass of the ethanol, c is its specific heat, and ΔT is the change in temperature. You can then calculate the amount of heat energy that must be removed from the ethanol to lower its temperature. You will then use the formula, q = mL, where mL is the latent heat of fusion of the ice, to calculate the mass of the ice cube.

 

[wais]

Hey there! It looks like you're having trouble with some phase change problems involving ethanol. Don't worry, I can help you out with these questions.

For the first question, we need to use the formula Q = m x c x ΔT, where Q is the amount of energy, m is the mass, c is the specific heat, and ΔT is the change in temperature. We also know that the energy needed for a phase change is equal to the molar heat of vaporization (ΔHvap) times the amount of substance (in moles). So, we can set up our equation like this:

Q(l to g) + Q(g to l) = ΔHvap x n

Where Q(l to g) is the energy needed to vaporize the liquid ethanol, Q(g to l) is the energy released when the vapor condenses back to liquid, and n is the number of moles of ethanol.

Now, let's plug in the values we know:

Q(l to g) = m x c x ΔT = (60g) x (2.6 g/(g degrees celsius)) x (52.3 - 12.3 degrees) = 7,800 J

Q(g to l) = m x c x ΔT = (6.66g) x (2.6 g/(g degrees celsius)) x (78.3 - 52.3 degrees) = 1,710.6 J

We can then combine these two equations and solve for ΔHvap:

7,800 J + 1,710.6 J = ΔHvap x n

9,510.6 J = ΔHvap x (6.66g / 46.07 g/mol) = ΔHvap x 0.1447 mol

ΔHvap = 9,510.6 J / 0.1447 mol = 65,742.5 J/mol

So, the molar heat of vaporization for ethanol is 65,742.5 J/mol.

For the second question, we can use a similar approach. We know that the energy released by the ethanol (ΔHfus) is equal to the energy absorbed by the ice (ΔHfus). We can set up our equation like this:

Q(ethanol) = -Q(ice)

Where Q(ethanol) is