How much heat (in kJ)is required to convert 2.565kg of liquid sulfur dioxide at the boiling point to a gas at 60C?

BP of SO2 is -10C and delta H vap is 25.73kJ/mol. Specific heat capacity of the gas is 0.622 J/g*K

I don't know what formula to use to calculate this problem??

I'm sure this will look familiar after you see it.

You remember the heat to raise the temperature of ice from -50 to steam at 300 C. This is done the same way.

q1 = heat to vaporize liquid SO2 at it boiling point.
q1 = mass liquid SO2 x heat vaporization.

q2 = heat to move vapor SO2 from its boiling point to 60 C.
q2 = mass vapor SO2 x specific heat SO2 gas x (Tfinal-Tinitial)

Total heat = q1 + q2
Watch the units. I would keep everything in grams and joules, then convert to the unit I wanted at the end after adding q1 and q2.

To calculate the heat required to convert liquid sulfur dioxide to a gas, we need to consider two processes: heating the liquid SO2 to its boiling point and then vaporizing it.

1. Step 1: Calculate the heat required to heat the liquid SO2 to its boiling point (from -10°C to the boiling point).

The formula to calculate the heat (Q) is given by Q = m * c * ΔT, where:
- m is the mass of the substance (in grams),
- c is the specific heat capacity of the substance (in J/g·°C),
- ΔT is the change in temperature (in °C).

However, in this case, the specific heat capacity is given in J/g·K, so we need to convert it to J/g·°C by using the conversion 1 K = 1°C. Therefore, in this case, c = 0.622 J/g·°C.

Given:
- Mass of liquid SO2 (m) = 2.565 kg = 2,565 g (since 1 kg = 1,000 g)
- Change in temperature (ΔT) = boiling point - initial temperature = -10°C - initial temperature

You didn't mention the initial temperature, so let's assume it is 25°C for demonstration purposes. Therefore, ΔT = -10°C - 25°C = -35°C.

Using the formula Q = m * c * ΔT:
Q1 = 2,565 g * 0.622 J/g·°C * (-35°C)

2. Step 2: Calculate the heat required to vaporize the liquid SO2 at its boiling point.

The formula for the heat (Q) in this case is given by Q = n * ΔHvap, where:
- n is the number of moles of the substance, which can be determined using the molar mass,
- ΔHvap is the enthalpy of vaporization per mole of the substance.

Given:
- Mass of liquid SO2 (m) = 2.565 kg = 2,565 g (as calculated before)
- Molar mass of SO2 = 32.07 g/mol (sulfur: 32.07 g/mol, oxygen: 16.00 g/mol * 2)
- ΔHvap = 25.73 kJ/mol = 25.73 × 10^3 J/mol

First, convert the mass of liquid SO2 (m) to moles using the molar mass:
n = m / Molar mass = 2,565 g / 32.07 g/mol

Using the formula Q2 = n * ΔHvap:
Q2 = (2,565 g / 32.07 g/mol) * 25.73 × 10^3 J/mol

Finally, to find the total heat required, add Q1 and Q2:
Total Heat Required = Q1 + Q2

Please note that you need to use the actual value for the initial temperature if it is provided, and make sure to use the correct units for your final answer (kJ in this case).