4 moles of water are heated from 240 K to 310. find delta entropy and graph entropy against K . Info : delta H fusion of water is 5 kJ/mol

delta H vaporization of water is 41.4 kJ/mol Cp of ice is 36 j/mol - k
Cp of water in liters is 74 j/mol-k

See:

http://www.jiskha.com/display.cgi?id=1233540017#1233540017.1233552198

To find the change in entropy (ΔS) when heating 4 moles of water from 240 K to 310 K, we can use the equation:

ΔS = ∫(Cp / T)dT

However, since the heat capacities (Cp) of water and ice are given in different units (joules per mole-kelvin and joules per mole-liter-kelvin), we need to convert them to the same units. Let's convert the heat capacities first:

Cp of ice = 36 J/mol-K
Cp of water = 74 J/mol-K (in liters)

To convert the Cp of water from liters to moles, we need to multiply it by the molar volume of water, which is approximately 18 mL/mol. Let's calculate the new Cp of water:

Cp of water (converted) = (74 J/mol-K) * (0.018 L/mol)
= 1.332 J/mol-K

Now that we have the heat capacities in the same units, we can proceed to find the change in entropy. Since the Cp is constant over this temperature range, we can simplify the equation:

ΔS = Cp * ln(T2 / T1)

Where T1 and T2 are the initial and final temperatures, respectively. Let's substitute the values:

ΔS = (1.332 J/mol-K) * ln(310 K / 240 K)
≈ 1.332 J/mol-K * ln(1.29167)
≈ 1.332 J/mol-K * 0.25436
≈ 0.3386 J/mol-K

Therefore, the change in entropy when heating 4 moles of water from 240 K to 310 K is approximately 0.3386 J/mol-K.

To graph the entropy against K, we can create a graph with temperature (K) on the x-axis and entropy (J/mol-K) on the y-axis. The graph will show how the entropy changes as temperature increases.

First, choose a range of temperatures, including the initial and final temperatures of 240 K and 310 K, respectively. Let's say we choose temperatures in intervals of 10 K.

Next, calculate the entropy at each temperature using the formula:

ΔS = Cp * ln(T / 240)

For example, at T = 240 K, the entropy is 0 J/mol-K since the temperature doesn't change. Then, calculate the entropy at T = 250, 260, 270, and so on until T = 310 K.

Finally, plot the temperatures on the x-axis and the corresponding entropy values on the y-axis to create the graph. Connect the points with a smooth line to visualize the change in entropy with increasing temperature.