A flask was immersed in 350 g of water at 25 degrees C. Steam at 100 degrees C was passed into this flask, and eventually condensed into water at 100 degrees C. If the temperature of the water surrounding the flask was raised to 70 degrees C, how many grams of steam must have condensed? (Assume that the condensed water remains at 100 degree C) (Specific heat of water: 4.184 J/g*C, H vap: 40.7 kJ/mol)
[350g H2O x specific heat H2O x (70-25)]+[mass steam x (heat vap)] + [mass H2O from steam x specific heat H2O x (70-100)] = 0
Solve for x = mass steam
The only unknown in that equation is mass steam and mass H2O from steam. I would let them = y and plug in the other numbers and solve for y. I think the answer will surprise you; i.e., less than you might think.
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.