To solve this problem, we need to calculate the heat gained and lost by the system.
First, let's break down the steps of the process:
1. The flask with water, initially at 25°C, is immersed in 350 g of water.
2. Steam at 100°C is passed into the flask, condensing into water at 100°C.
3. The surrounding water is heated to 70°C.
Now, let's calculate the heat gained and lost for each step:
Step 1: Heating the flask and water to 100°C
To calculate the heat gained by the flask and the initial water, we can use the equation:
q = m * c * ΔT
where q is the heat gained or lost, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The heat gained by the flask and the initial water can be calculated as follows:
q1 = m1 * c * ΔT1
q1 = (m flask + m initial ) * c * (100°C - 25°C)
q1 = (m flask + 350 g) * 4.184 J/g°C * 75°C
Step 2: Condensing the steam
To calculate the heat released by the condensing steam, we can use the equation:
q = n * ΔH
where q is the heat gained or lost, n is the number of moles, and ΔH is the enthalpy of vaporization.
The heat released by the condensing steam can be calculated as follows:
q2 = n * ΔH
q2 = (m steam / M steam ) * ΔH
To convert kJ/mol to J/g:
ΔH = 40.7 kJ/mol = 40.7 × 10^3 J/mol
Step 3: Heating the surrounding water to 70°C
To calculate the heat lost by the surrounding water, we can use the equation:
q = m * c * ΔT
The heat lost by the surrounding water can be calculated as follows:
q3 = m3 * c * ΔT3
q3 = 350 g * 4.184 J/g°C * (70°C - 25°C)
Now, let's find the total heat gained and lost by the system:
The total heat gained by the system is equal to the heat gained by the flask and initial water (q1) and the heat gained by the condensing steam (q2):
q gained = q1 + q2
The total heat lost by the system is equal to the heat lost by the surrounding water (q3):
q lost = q3
Since the total heat gained must be equal to the total heat lost, we can set up the equation:
q gained = q lost
q1 + q2 = q3
By substituting the equations we derived earlier and solving for m steam, we can find the mass of steam condensed.