A block of ice of temperature 0°C and mass20g was placed in a beaker and weighed. The total mass was 55g. Steam at 110°C was ducted into the ice until the ice completely melted. Assuming no loss of heat to the surroundings, find the mass of the beaker and its contents
To find the mass of the beaker and its contents, we can use the principle of conservation of mass. This principle states that the total mass of a closed system remains constant, even if physical or chemical changes occur.
In this case, we have a closed system consisting of the block of ice, the beaker, and the steam. We can track the mass changes at each stage of the process to find the final mass of the system.
Step 1: The initial mass of the closed system is 55g, which includes the ice and the beaker.
Step 2: The ice absorbs heat from the steam and begins melting. During this phase change, the temperature of the ice remains constant at 0°C until all the ice is completely melted.
Step 3: After all the ice has melted, the resulting liquid water will have a mass equal to the initial mass of the ice. This means the mass of the water is 20g.
Step 4: In the final stage, the steam condenses into liquid water as it loses heat to the system. This will increase the mass of the water in the system.
To find the final mass of the system, we need to consider the mass change of the steam during condensation. We can use the equation m1v1 = m2v2, where m1 and v1 are the initial mass and volume of the steam, and m2 and v2 are the final mass and volume of the condensed liquid water.
The initial volume of the steam can be calculated using the ideal gas law:
PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Given that the temperature is 110°C (which is equivalent to 383K), we can assume the pressure remains constant. Let's say the volume of the steam is V1.
Therefore, using the ideal gas law, we have:
(P x V1) = n x R x T
(P x V1) = n x R x 383
Now, let's assume that all the steam condenses and becomes liquid water. The final mass of the system will be the sum of the initial mass of the water (20g) and the mass of the condensed steam.
Now, we need to find the mass of the condensed steam (m2). Rearranging the equation m1v1 = m2v2, we have m2 = (m1v1) / v2.
Substituting the initial mass of the steam (m1 = n x molar mass of water) and the initial volume (v1 = V1), we can solve for m2.
After we calculate m2, the final mass of the system will be the sum of the initial mass of the water (20g) and m2. This will give us the mass of the beaker and its contents.
To solve this problem, we can consider the heat exchange that occurs during the process.
Step 1: Calculate the heat required to melt the ice.
The heat required to melt the ice can be calculated using the formula:
Q = m * L
where:
Q is the heat required (in joules)
m is the mass of the ice (in grams)
L is the specific heat of fusion for ice, which is 334 J/g
In this case, the mass of the ice is 20g, so the heat required to melt the ice is:
Q = 20g * 334 J/g = 6680 J
Step 2: Calculate the heat released when the steam condenses to water.
The heat released when the steam condenses to water can be calculated using the formula:
Q = m * L
where:
Q is the heat released (in joules)
m is the mass of the water (in grams)
L is the specific heat of condensation for steam, which is -2260 J/g
Since the temperature of the steam is 110°C and it condenses to water at 0°C, the change in temperature is 110°C - 0°C = 110°C.
Since the specific heat capacity of the water is 4.18 J/g°C, we can calculate the mass of the water using the formula:
Q = m * C * ΔT
where:
Q is the heat released (in joules, which is equal to 6680 J)
C is the specific heat capacity of water (in J/g°C)
ΔT is the change in temperature (in °C)
Simplifying this equation, we have:
6680 J = m * 4.18 J/g°C * 110°C
m = 6680 J / (4.18 J/g°C * 110°C)
m = 14.39 g
Step 3: Calculate the mass of the beaker and its contents.
The total mass of the beaker and its contents is given as 55g. Since the mass of the ice was 20g and the mass of the water is 14.39g, we can calculate the mass of the beaker using the equation:
Mass of beaker = Total mass - Mass of ice - Mass of water
Mass of beaker = 55g - 20g - 14.39g
Mass of beaker = 20.61g
So, the mass of the beaker and its contents is approximately 20.61g.