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Multiple Choice
If 45.0 mL of ethanol (density = 0.789 g/mL) initially at 9.0 °C is mixed with 45.0 mL of water (density = 1.0 g/mL) initially at 28.2 °C in an insulated beaker, what is the final temperature of the mixture, assuming that no heat is lost?
A
15.0 °C
B
20.0 °C
C
22.5 °C
D
18.6 °C
Verified step by step guidance
1
Calculate the mass of ethanol using its volume and density. Use the formula: mass = volume × density. For ethanol, mass = 45.0 mL × 0.789 g/mL.
Calculate the mass of water using its volume and density. Use the formula: mass = volume × density. For water, mass = 45.0 mL × 1.0 g/mL.
Use the specific heat capacities of ethanol and water to set up the heat transfer equation. The specific heat capacity of ethanol is approximately 2.44 J/g°C, and for water, it is 4.18 J/g°C.
Set up the heat transfer equation assuming no heat is lost: (mass of ethanol) × (specific heat of ethanol) × (change in temperature of ethanol) + (mass of water) × (specific heat of water) × (change in temperature of water) = 0.
Solve the equation for the final temperature of the mixture. The change in temperature for each substance is the final temperature minus the initial temperature. Rearrange the equation to find the final temperature.