Show the calculation of the final temperature of the mixture when a 40.5 gram sample of water at 85.7°C is added to a 35.8 gram sample of water at 26.3°C in a coffee cup calorimeter.

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High School

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AsherIsaiah AsherIsaiah · Answer 1 · 2024-05-11T11:32:54-04:00

The final temperature of the mixture is 50.0°C.

To calculate the final temperature of the mixture, we can use the equation:

m1c1ΔT1 + m2c2ΔT2 = 0

Where:

m1 = mass of the first sample of water = 40.5 grams
c1 = specific heat capacity of water = 4.18 J/g°C
ΔT1 = change in temperature of the first sample = final temperature - initial temperature = final temperature - 85.7°C
m2 = mass of the second sample of water = 35.8 grams
c2 = specific heat capacity of water = 4.18 J/g°C
ΔT2 = change in temperature of the second sample = final temperature - initial temperature = final temperature - 26.3°C

Substituting the given values into the equation, we get:

(40.5g)(4.18 J/g°C)(final temperature - 85.7°C) + (35.8g)(4.18 J/g°C)(final temperature - 26.3°C) = 0

Simplifying the equation, we can solve for the final temperature:

167.79(final temperature) - 14395.77 + 150.04(final temperature) - 1489.94 = 0

317.83(final temperature) = 15885.71

final temperature = 15885.71 / 317.83

= 50.0°C

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