An ice cube at 0 degrees Celsius was dropped into 30.0 g of water in a cup at 45.0 degrees Celsius. At the instant that all of the ice was melted, the temperature of the water i the cup was 19.5 degrees Celsius. What was the mass of the ice cube?
hello scoob thx for pickin jiskha:)
!!best homework help ever!!
uhh ur best options are:
a}google it
b}post same question 2mmorow when there are more tutors on line people who can help with chemistry :)
How much heat did the water lose?
mass water x specific heat water x (Tfinal-Tinitial).
How much heat did the ice gain?
mass ice x heat fusion.
The sum of those should be zero.
just use heat gain by ice =heat lost by water.
To find the mass of the ice cube, we can use the principle of conservation of energy. The heat lost by the water as it cools down will be equal to the heat gained by the ice cube as it melts. We can use the equation:
Q_lost = Q_gained
The heat lost by the water (Q_lost) can be calculated using the formula:
Q_lost = mass_water * specific_heat_water * (final_temperature - initial_temperature)
The specific heat capacity of water is approximately 4.18 J/g°C.
The heat gained by the ice cube (Q_gained) can be calculated using the formula:
Q_gained = mass_ice * heat_fusion_ice
The heat of fusion for ice is approximately 333.5 J/g.
Since we know the initial and final temperatures of the water, as well as the mass of the water, we can calculate the heat lost by the water. Then, we can rearrange the equation to solve for the mass of the ice cube (mass_ice).
Let's calculate it step by step:
1. Calculate the heat lost by the water:
Q_lost = mass_water * specific_heat_water * (final_temperature - initial_temperature)
mass_water = 30.0 g
specific_heat_water = 4.18 J/g°C
final_temperature = 19.5°C
initial_temperature = 45.0°C
Q_lost = 30.0 g * 4.18 J/g°C * (19.5°C - 45.0°C)
2. Calculate the heat gained by the ice cube:
Q_gained = mass_ice * heat_fusion_ice
heat_fusion_ice = 333.5 J/g
3. Set the heat lost to be equal to the heat gained:
mass_water * specific_heat_water * (final_temperature - initial_temperature) = mass_ice * heat_fusion_ice
Now we need to rearrange the equation to solve for mass_ice:
mass_ice = (mass_water * specific_heat_water * (final_temperature - initial_temperature)) / heat_fusion_ice
Simply plug in the known values and calculate:
mass_ice = (30.0 g * 4.18 J/g°C * (19.5°C - 45.0°C)) / 333.5 J/g
mass_ice ≈ 10.134 g
Therefore, the mass of the ice cube is approximately 10.134 grams.