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Water has a specific heat of 4.186 J/g°C, and ethanol has a specific heat of 2.450 J/g°C. Based on this information, which best compares water and ethanol?

It requires more heat to raise the temperature of a gram of ethanol by 1°C.
There are more molecules in a gram of water.
Ethanol has a lower formula mass.
Water has more protons and neutrons in its nuclei.

1 answer

To compare water and ethanol based on the provided specific heat capacities and other considerations, let's evaluate each statement:

  1. It requires more heat to raise the temperature of a gram of ethanol by 1°C.

    • This statement is false. Water has a higher specific heat capacity (4.186 J/g°C) than ethanol (2.450 J/g°C), which means it requires more heat to raise the temperature of a gram of water by 1°C than it does for ethanol.

  2. There are more molecules in a gram of water.

    • To assess this, we can calculate the number of moles in a gram of each substance.
      • The molar mass of water (H₂O) is approximately 18 g/mol, so 1 gram of water contains about \( \frac{1 , \text{g}}{18 , \text{g/mol}} \approx 0.0556 , \text{mol} \) of water molecules.
      • The molar mass of ethanol (C₂H₅OH) is approximately 46 g/mol, so 1 gram of ethanol contains about \( \frac{1 , \text{g}}{46 , \text{g/mol}} \approx 0.0217 , \text{mol} \) of ethanol molecules.
    • Since 0.0556 mol > 0.0217 mol, this statement is true: there are more molecules in a gram of water than in a gram of ethanol.

  3. Ethanol has a lower formula mass.

    • This statement is also true. The molar mass of ethanol (46 g/mol) is higher than that of water (18 g/mol), so this statement is false.

  4. Water has more protons and neutrons in its nuclei.

    • Water has 2 hydrogen atoms (1 proton each) and 1 oxygen atom (8 protons). Therefore, water has a total of 10 protons. In terms of neutrons, oxygen has 8 neutrons (roughly) and hydrogen has none. So, water has a total of about 18 nucleons (protons + neutrons).
    • Ethanol, with its molecular formula C₂H₅OH, consists of 2 carbon atoms (6 protons total), 6 hydrogen atoms (6 protons), and 1 oxygen atom (8 protons), totaling 20 protons. Oxygen has 8 neutrons, and each carbon has around 6 neutrons (so 12 neutrons for 2 carbons), leading to 32 nucleons for ethanol.
    • So, ethanol actually has more protons and neutrons compared to water, making this statement false.

In conclusion, the best comparison based on the provided information is:

There are more molecules in a gram of water.