35g of water at 55 degrees Celsius is heated until it is all steam at 100 degrees Celsius. How much every was added?
q1 = heat to move H2O from 55 to 100 C.
q1 = mass x specific heat liqud water x (Tfinal-Tinial). Tfinal = 100; Tinitial = 55.
q2 = heat to vaporize liquid water to steam @ 100 C.
q2 = mass water x heat vaporization.
total q = q1 + q2.
To solve this problem, you need to calculate the amount of energy required to heat the water from 55 degrees Celsius to 100 degrees Celsius and then determine how much water was needed to absorb this energy.
Here's how you can approach the problem step by step:
Step 1: Calculate the energy required to heat the water.
The specific heat capacity of water is 4.18 J/g°C. To calculate the energy required to heat the water, you can use the formula:
Q = m * c * ΔT
Where:
Q is the heat energy in Joules,
m is the mass of the water in grams,
c is the specific heat capacity of water (4.18 J/g°C), and
ΔT is the change in temperature (100°C - 55°C = 45°C).
Using this formula, calculate the energy required to heat the water from 55°C to 100°C.
Q = 35 g * 4.18 J/g°C * 45°C
Step 2: Convert the energy required to heat the water to the amount of water evaporated.
The heat energy required to convert water to steam is known as enthalpy of vaporization. For water, it is approximately 40.7 kJ/g (kilojoules per gram). To convert the energy required to heat the water to the amount of water evaporated, use the formula:
Q = m * ΔH
Where:
Q is the heat energy in Joules,
m is the mass of the water evaporated in grams, and
ΔH is the enthalpy of vaporization (40.7 kJ/g).
First, convert the heat energy required to heat the water from Joules to kilojoules:
Q = (35 g * 4.18 J/g°C * 45°C) / 1000
Then, divide the converted energy by the enthalpy of vaporization to determine the mass of water evaporated:
m = Q / ΔH
Step 3: Calculate the mass of water evaporated in grams.
Plug in the values into the formula:
m = Q / ΔH
m = [(35 g * 4.18 J/g°C * 45°C) / 1000] / 40.7 kJ/g
Finally, calculate the mass of water evaporated.
m = (35 g * 4.18 J/g°C * 45°C) / (40.7 kJ/g * 1000 g)
After performing the calculations, you will find the mass of water evaporated. This will tell you how much water was added to convert 35g of water at 55 degrees Celsius to all steam at 100 degrees Celsius.