Final answer:
To find the final temperature of water after burning benzene, we calculate the energy released by 6.65 g of benzene, convert it to joules, and apply it to the water's specific heat capacity formula. A change in temperature of 11.73°C is found, leading to a final temperature of 32.73°C.
Step-by-step explanation:
To solve for the final temperature of water after burning benzene (C₆H₆), we must apply the concept of energy transfer and the specific heat capacity of water. Given that one mole of C₆H₆ releases 3.27 MJ when burned, we first need to determine the amount of energy released by burning 6.65g of C₆H₆.
One mole of C₆H₆ has a mass of 78.11 g/mol. Therefore, the energy released by burning 6.65 g of benzene is:
(6.65 g / 78.11 g/mol) × 3.27 MJ/mol = 0.279 MJ.
Next, we convert this energy to joules since the specific heat capacity of water is typically given in J/g°C:
0.279 MJ × 10¶ J/MJ = 279,000 J.
The energy transferred to the water can be calculated using the specific heat formula:
q = mc∆T, where m is mass, c is specific heat, and ∆T is change in temperature.
For water, c is typically 4.18 J/g°C. Rearranging the formula to solve for ∆T gives us:
∆T = q / (mc), so the change in temperature of the water is:
∆T = 279,000 J / (5,690 g × 4.18 J/g°C) = 279,000 J / 23,789.2 J/°C = 11.73 °C.
Adding this change in temperature to the initial temperature of the water gives the final temperature:
21°C + 11.73°C = 32.73°C.
Therefore, the final temperature of the water after burning 6.65 g of benzene is 32.73°C.