Final answer:
To change 48.5 g of liquid mercury at 400 K to vapor at 700 K, a total heat of 10618 J is required.
Step-by-step explanation:
To calculate the amount of heat required to change liquid mercury at 400 K to vapor at 700 K, we need to consider the heat needed for two processes: raising the temperature of the liquid mercury to its boiling point and then converting it to vapor. First, we need to calculate the heat required to raise the temperature of 48.5 g of mercury from 400 K to its boiling point of 629.88 K. We can use the formula Q = m * c * ΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. The specific heat capacity of mercury is 0.14 J/g-K, so the heat required to raise the temperature is:
Q = 48.5 g * 0.14 J/g-K * (629.88 K - 400 K) = 6504 J.
Next, we need to calculate the heat required for the phase change from liquid to vapor. We can use the formula Q = m * Lv, where Lv is the heat of vaporization. The heat of vaporization of mercury is 17.0 kJ/mol. First, we need to convert the mass of mercury to moles:
moles = 48.5 g / (200.59 g/mol) = 0.242 mol.
Now we can calculate the heat required for the phase change:
Q = 0.242 mol * 17.0 kJ/mol = 4.114 kJ = 4114 J.
Finally, we can add the heat required for raising the temperature and the heat required for the phase change:
Total heat = 6504 J + 4114 J = 10618 J.