If 55.0 mL of ethanol (density = 0.789 g/mL) initially at 8.0 °C is mixed with 55.0 mL of water (density = 1.0 g/mL) initially at 28.0 °C in an insulated beaker, what is the final temperature of the mixture, assuming that no heat is lost to the surroundings?

• A. 18.0 °C
• B. 15.0 °C
• C. 20.0 °C
• D. 22.0 °C

Answer: (A)

Verified step by step guidance

1. Calculate the mass of ethanol using its volume and density. Use the formula: mass = volume × density. For ethanol, this is 55.0 mL × 0.789 g/mL.
2. Calculate the mass of water using its volume and density. Use the formula: mass = volume × density. For water, this is 55.0 mL × 1.0 g/mL.
3. Use the specific heat capacities of ethanol and water to set up the heat balance equation. The specific heat capacity of ethanol is approximately 2.44 J/g°C and for water, it is 4.18 J/g°C.
4. Set up the heat balance equation assuming no heat is lost to the surroundings: (mass of ethanol × specific heat of ethanol × (final temperature - initial temperature of ethanol)) + (mass of water × specific heat of water × (final temperature - initial temperature of water)) = 0.
5. Solve the heat balance equation for the final temperature of the mixture. This involves substituting the known values and solving for the unknown final temperature.