Question

The enthalpy change for converting 1.00 mol of ice at -50.0°c to water at 70.0°c is __________ kj. the specific heats of ice, water, and steam are 2.09 j/g-k, 4.18 j/g-k, and 1.84 j/g-k, respectively. for h2o, hfus = 6.01 kj/mol, and hvap = 40.67 kj/mol

Answer 1

To calculate the enthalpy change, we add the energy required to heat the ice to 0°C, the enthalpy of fusion to melt the ice, and the energy required to heat the resulting water to 70.0°C. The total enthalpy change is 6.4071 kJ.

Step-by-step explanation:

To calculate the enthalpy change for converting 1.00 mol of ice at -50.0°C to water at 70.0°C, we must account for several steps, involving heating the ice, melting it, and then heating the resulting water. The specific heats and enthalpies of phase changes are provided, so we can use these to calculate the total energy change in kilojoules (kJ).

1. Heating ice from -50.0°C to 0°C: Q1 = m × Cice × ΔT
2. Melting the ice at 0°C to water: Q2 = m × ΔHfus
3. Heating water from 0°C to 70.0°C: Q3 = m × Cwater × ΔT

In these equations, m is the number of moles (1.00 mol), Cice and Cwater are the specific heats of ice and water, respectively, ΔT is the temperature change, and ΔHfus is the molar heat of fusion.

Let's do the calculation now:

1. Q1 = (1.00 mol) × (2.09 J/g°C/mol) × (50.0°C) = 104.5 J
2. Q2 = (1.00 mol) × (6.01 kJ/mol) = 6.01 kJ
3. Q3 = (1.00 mol) × (4.18 J/g°C) × (70.0°C) = 292.6 J

Remember to convert all the energy values to kJ:

• Q1 in kJ = 104.5 J / 1000 = 0.1045 kJ
• Q3 in kJ = 292.6 J / 1000 = 0.2926 kJ

To find the total enthalpy change, sum up all the heats:

Total enthalpy change = Q1 + Q2 + Q3 = 0.1045 kJ + 6.01 kJ + 0.2926 kJ = 6.4071 kJ.

Answer 2

First, calculate for the amount of heat used up for increasing the temperature of ice.

H = mcpdT
H = (18 g)*(2.09 J/g-K)(50 K) = 1881 J

Then, solve for the heat needed to convert the phase of water.
H = (1 mol)(6.01 kJ/mol) = 6.01 kJ = 6010 J

Then, solve for the heat needed to increase again the temperature of water.
H = (18 g)(4.18 J/gK)(70 k)
H = 5266.8 J

The total value is equal to 13157.8 J

Answer: 13157.8 J