Question

How much heat in kilojoules is evolved in converting 2.00 mol of steam at 150 ∘C to ice at -55.0 ∘C? The heat capacity of steam is 1.84 J/g∘C and that of ice is 2.09 J/g∘C.

Remember that if heat is leaving the system, then q is a negative number and if heat is entering the system, then q is a positive number.

Answer 1

To find the heat evolved in converting steam to ice, we need to consider the heat absorbed in three steps: heating the steam to 0°C, melting the ice, and finally cooling the water to -55.0°C. The heat evolved is approximately 235.92 kJ.

Step-by-step explanation:

To find the heat evolved in converting steam to ice, we need to consider the heat absorbed in three steps: heating the steam to 0°C, melting the ice, and finally cooling the water to -55.0°C. We can calculate the heat absorbed in each step using the given heat capacities of steam and ice.

First, we calculate the heat absorbed in heating the steam from 150°C to 0°C. The formula for calculating heat is Q = mcΔT, where Q is the heat, m is the mass, c is the heat capacity, and ΔT is the change in temperature.

The heat absorbed in heating the steam is Q = (2.00 mol)(18.02 g/mol)(1.84 J/g°C)(0 - 150°C) = -5,232.48 J. Since heat is leaving the system, the heat absorbed is a negative value.

Next, we calculate the heat absorbed in melting the ice at 0°C. The formula for calculating heat is Q = mL, where Q is the heat, m is the mass, and L is the heat of fusion.

Using the given information, the heat absorbed in melting the ice is Q = (100 g)(2.09 J/g°C) = 209.0 J.

Finally, we calculate the heat absorbed in cooling the water from 0°C to -55.0°C. The formula for calculating heat is Q = mcΔT, where Q is the heat, m is the mass, c is the heat capacity, and ΔT is the change in temperature.

The heat absorbed in cooling the water is Q = (100 g)(4.18 J/g°C)(-55.0 - 0°C) = -229,900 J. Since heat is leaving the system, the heat absorbed is a negative value.

To find the total heat absorbed in all three steps, we add the heats together: -5,232.48 J + 209.0 J - 229,900 J = -235,923.48 J.

To convert the heat from joules to kilojoules, we divide by 1000: -235,923.48 J / 1000 = -235.92 kJ.

Therefore, the heat evolved in converting 2.00 mol of steam at 150°C to ice at -55.0°C is approximately 235.92 kJ.

Answer 2

= 115.898 kJ

Step-by-step explanation:

Heat evolved in converting 2.00 mol of steam at 150 ∘C to ice at -55.0 ∘C

Will be calculated in steps

Step 1; Heat evolved by steam from 150°C to 100°C

Heat = (2×18) g × 1.84 J/g°C × (150 -100)

= 3312 Joules

Step 2; Heat required to convert steam to water without change in temperature;

Heat = moles × Molar Latent heat of vaporization.

= 2 moles × 4.07 ✕ 104 J/mol

= 8.14 × 10^4 Joules

Step 3: Heat evolved by water from 100°C to 0°C.

Heat = mass × specific heat capacity × ΔT

= (2 × 18) × 4.18 J/g°C × 100

= 15,048 Joules

Step 4; Heat evolved in converting water at 0°C to ice at 0°

Heat = number of moles × molar latent heat of fusion

= 2 moles × 6000 j/mole

= 12 000 Joules

Step 5, heat evolved in converting ice at 0°C to -55°C

Heat = mass × specific heat capacity × ΔT

= (2×18) × 2.09 j/g°C × 55

= 4138.2 Joules

Total amount of heat evolved;

= 3312 J + 8.14 × 10^4 J + 15,048 J + 12 000 J + 4138.2 J

= 115,898.2 joules

= 115.898 kJ