How many joules are needed to change 163.34 g of water at 54.1 °C to steam at 100 °C?

To calculate the amount of energy required to change a substance from one phase to another, we need to use the formula:

Q = m × ΔH

where:
Q is the energy needed (in joules)
m is the mass of the substance (in grams)
ΔH is the heat of transformation (also known as the heat of fusion or heat of vaporization, depending on the specific phase change)

In this case, we want to calculate the energy required to change water from a liquid phase to a gaseous phase (steam). We need to consider two steps: first, we need to heat the water from its initial temperature to its boiling point, and then we need to convert it from water at its boiling point to steam.

Step 1: Heating the water to its boiling point (54.1 °C to 100 °C)
For this step, we use the formula:

Q1 = m × c × ΔT

where:
Q1 is the energy needed to heat the substance (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in joules/gram·°C)
ΔT is the change in temperature (final temperature - initial temperature)

The specific heat capacity of water is approximately 4.18 J/g·°C.

Using the formula:

Q1 = 163.34 g × 4.18 J/g·°C × (100 °C - 54.1 °C)

Q1 = 163.34 g × 4.18 J/g·°C × 45.9 °C

Q1 ≈ 31694.972 J (rounded to the nearest joule)

Step 2: Condensing the water to steam at its boiling point (100 °C)
For this step, we use the formula:

Q2 = m × ΔHvap

where:
Q2 is the energy needed for the phase change (in joules)
m is the mass of the substance (in grams)
ΔHvap is the heat of vaporization of the substance (in joules/gram)

The heat of vaporization for water is approximately 2260 J/g.

Using the formula:

Q2 = 163.34 g × 2260 J/g

Q2 ≈ 368070.4 J (rounded to the nearest joule)

Now, to find the total energy required, we sum up the results from Step 1 and Step 2:

Q_total = Q1 + Q2

Q_total = 31694.972 J + 368070.4 J

Q_total ≈ 399765.372 J (rounded to the nearest joule)

Therefore, approximately 399,765 joules of energy are needed to change 163.34 grams of water at 54.1 °C to steam at 100 °C.