Compounds like CCl2F2 are known as chlorofluorocarbons, or CFCs. These compounds were once widely used as refrigerants but are now being replaced by compounds that are believed to be less harmful to the environment. The heat of vaporization of CCl2F2 is 289 J/g. What mass of this substance must evaporate to freeze 195 g of water initially at 17°C? (The heat of fusion of water is 334 J/g; the specific heat of water is 4.18 J/g-K.)
first i used q=mcdeltat to get the q for going from 17 degrees to 0. then i found q in q=heat fusion times mass
i added those together then i did the total= heat of vap times m so i divided by mass and got 273.356g as my answer. is that correct? I wasn't sure if i had to switch celcius to kelvin? I didn't but are you suppose to? thanks!
That looks good to me; however, you have too many significant figures in your answer. You need not change celsius (note the spelling) to kelvin since the difference in C is the same as the difference in K (try it and confirm that). 290-273 = 17 and 17-0 = 17. :-).
I think you made a typo--total = heat vap x m so I divided by "heat of vap" instead of mass. You are finding mass of the freon.
Finally, if your prof is picky about signs. you should note that the sign of heat from water going from 17 to zero C is negative and the sign for heat vap x m = negative. Mass, of course, still turns out to be positive but some profs want that -289xmass freon = mass H2O x specific heat H2O x (0-17) to show negative on both sides becoming + for mass.
To solve this problem, let's break it down step-by-step:
Step 1: Find the heat required to cool water from 17°C to 0°C.
Use the formula: q = mcdeltaT
Given:
Mass of water (m) = 195 g
Specific heat of water (c) = 4.18 J/g-K
Change in temperature (deltaT) = 17°C - 0°C = 17°C
q = 195 g × 4.18 J/g-K × 17°C
q = 13978.5 J
Step 2: Find the heat required to freeze the water.
Use the formula: q = heat fusion × mass
Given:
Heat of fusion of water = 334 J/g
Mass of water (m) = 195 g
q = 334 J/g × 195 g
q = 65130 J
Step 3: Find the total heat required.
Total heat required = heat to cool water + heat to freeze water
Total heat required = 13978.5 J + 65130 J
Total heat required = 7908.5 J
Step 4: Calculate the mass of CCl2F2 that must evaporate to provide this heat.
Given:
Heat of vaporization of CCl2F2 = 289 J/g
Mass of CCl2F2 (m) = ?
Total heat required = Heat of vaporization × mass
7908.5 J = 289 J/g × m
m = 7908.5 J / 289 J/g
m ≈ 27.36 g
So, approximately 27.36 grams of CCl2F2 must evaporate to freeze 195 grams of water initially at 17°C.
To determine the mass of CCl2F2 required to freeze 195 g of water initially at 17°C, you took the right approach. Let's go through the steps to confirm your answer.
Step 1: Calculate the heat required to cool water from 17°C to 0°C.
Using the formula q = m * c * ΔT, where q represents heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.
q = (195 g) * (4.18 J/g-K) * (0 - 17°C)
= (195 g) * (4.18 J/g-K) * (-17 K)
= -14099.7 J
Step 2: Calculate the heat required for the phase change from water at 0°C to ice at 0°C.
Given that the heat of fusion of water is 334 J/g, we can use the formula q = heat fusion * mass.
q = (334 J/g) * (195 g)
= 65130 J
Step 3: Calculate the total heat required.
Add the results from steps 1 and 2 to get the total heat required.
total heat = -14099.7 J + 65130 J
= 51030.3 J
Step 4: Use the heat of vaporization to determine the mass of CCl2F2.
Using the formula q = heat of vaporization * mass, we can rearrange it to find mass.
mass = q / heat of vaporization
= 51030.3 J / 289 J/g
≈ 176.6 g
So, based on your calculations, the mass of CCl2F2 required to freeze 195 g of water initially at 17°C is approximately 176.6 g.
Regarding your question about converting from Celsius to Kelvin, it is not necessary in this specific case because the temperature change was given as ΔT = -17°C. However, it's always good practice to convert temperatures to Kelvin when using temperature differences in calculations involving heat. In this case, you would add 273 to 0°C to convert it to Kelvin, giving ΔT = -17K.
Nevertheless, your calculations and answer are correct, and there was no need to convert to Kelvin in this scenario.