what is the final temperature of amixture containning 25 grams of ice at -20 degree celciusadded to water at room temperature 22oC mass of water is 50g
followed the steps given by you
but not getting the answer (0degree celsius)
That's because I assumed, incorrectly, that all of the ice would melt. It won't.
How many J does it take to move T of ice at -20C to OC? That's
q = (mass ice x specific heat ice x (Tf-Ti) = [25g x 2.01 J/g x (20)] = 1005 J.
How much will that lower the T of the water?
1005 = mass H2O x specific heat H2O x delta T and solve for delta T. I obtained about 4.8 C so T H2O now 22-4.8 = about 17.2.
So how many J do you have in the H2O @ 17.2 C to lose? That's [mass H2O x specific heat H2O x (Tf-Ti)] = 50*4.184 x (17.2) = 3598 if the H2O moves T all the way to zero C. Now, how much ice will that melt at zero C? That's
3698 = mass ice x heat fusion
3698 = mass ice x 334
mass ice = 3698/334 = approx 11g ice which will leave 25 - about 11 = about 14g unmelted.
So you will have water at zero with 14 g ice floating.
I didn't realize all of the ice didn't melt until I started on the problem an came out with a negative value for Tf.
To calculate the final temperature of a mixture, you can use the principle of energy conservation, which states that the total energy before mixing is equal to the total energy after mixing.
Here's how you can approach this problem step by step:
Step 1: Calculate the energy gained or lost by the ice:
- The specific heat capacity of ice is 2.09 J/g°C.
- The initial temperature of the ice is -20°C.
- The final temperature of the ice would be 0°C (since it will melt to water).
- The energy gained or lost by the ice can be calculated using the formula:
Energy = mass × specific heat capacity × change in temperature.
Substitute the values into the formula:
Energy = 25g × 2.09 J/g°C × (0°C - (-20°C))
Calculate the energy gained or lost by the ice.
Step 2: Calculate the energy gained or lost by the water:
- The specific heat capacity of water is 4.18 J/g°C.
- The initial temperature of the water is 22°C.
- The final temperature of the water would be the same as the final temperature of the mixture.
- The energy gained or lost by the water can be calculated using the formula:
Energy = mass × specific heat capacity × change in temperature.
Substitute the values into the formula:
Energy = 50g × 4.18 J/g°C × (final temperature - 22°C)
Calculate the energy gained or lost by the water.
Step 3: Set up the equation:
According to the principle of energy conservation, the energy gained by the ice should be equal to the energy gained by the water. So, you can set up the equation as follows:
Energy gained or lost by ice = Energy gained or lost by water
Set the two calculated energies equal to each other and solve for the final temperature of the mixture.
If you are not getting the final temperature of 0°C, please double-check the calculations in Step 1 and Step 2 to ensure all values are correctly substituted and the math is done accurately.