Determine the melting temperature when 150.00g of ice at 0 degree celdius is mixed with 300g of water at 50 degree celsius?
heat of fusion * 150 g + 150 * heat capacity* (T-0) = 300 * heat capacity*(50-T)
To determine the melting temperature when ice and water are mixed, we need to consider the process of energy transfer during the phase change.
First, let's calculate the energy required to heat the water from 0°C to its melting temperature, which is 0°C.
The specific heat capacity of water is 4.18 J/g°C, so the energy (Q) needed to heat the water can be calculated using the following formula:
Q = m * c * ΔT
Where:
Q = heat energy (in joules)
m = mass of water (in grams)
c = specific heat capacity of water (in J/g°C)
ΔT = change in temperature (in °C)
Given:
Mass of water (m) = 300 g
Specific heat capacity of water (c) = 4.18 J/g°C
Change in temperature (ΔT) = Melting temperature (0°C) - Initial temperature (50°C) = -50°C
Q = 300 g * 4.18 J/g°C * (-50°C)
Q = -62700 J
The negative sign indicates that the water is losing energy as it cools down.
Next, we need to calculate the energy released when the ice at 0°C melts and reaches the same temperature as the water.
The heat of fusion (Hf) for ice is 334 J/g. So the energy (Q) released during this phase change can be calculated using the formula:
Q = m * Hf
Where:
Q = heat energy (in joules)
m = mass of ice (in grams)
Hf = heat of fusion (in J/g)
Given:
Mass of ice (m) = 150.00 g
Heat of fusion (Hf) = 334 J/g
Q = 150.00 g * 334 J/g
Q = 50100 J
Lastly, we need to determine the final temperature when the ice completely melts and mixes with the water.
The total energy change (ΔE) is the sum of the energy gained by cooling the water and the energy released during the phase change:
ΔE = Q (energy gained by cooling) + Q (energy released during phase change)
ΔE = (-62700 J) + (50100 J)
ΔE = -12600 J
Now, let's calculate the final temperature (Tf) using the formula:
ΔE = m * c * ΔT
-12600 J = (300 g + 150.00 g) * c * ( Tf - 0°C)
Simplifying the equation:
-12600 J = 450 g * c * Tf
Finally, rearrange the equation to solve for Tf:
Tf = -12600 J / (450 g * c)
Plugging in the value for the specific heat capacity of water (c = 4.18 J/g°C), we get:
Tf = -12600 J / (450 g * 4.18 J/g°C)
Tf = -7.15°C
Thus, the final temperature when the ice and water are mixed is approximately -7.15°C.