The sun bombards the earth with about 1KJ m^-2s^-1. Calculate the maximum mass of pure ethanol that can be vaporized in 10 min from a beaker left in strong sunshine, assuming the surface area of the ethanol t be 50cm^2.
To calculate the maximum mass of pure ethanol that can be vaporized in 10 min from a beaker left in strong sunshine, we need to find the amount of energy received from the sun and then determine how much energy is required to vaporize ethanol.
Step 1: Calculate the energy received from the sun.
The energy received from the sun is given as 1 KJ m^-2 s^-1. This means that every square meter of area receives 1 KJ of energy every second. However, we need to find the energy received in 10 minutes, which is 10 minutes * 60 seconds/minute = 600 seconds.
So, the energy received from the sun in 10 minutes on an area of 50 cm^2 (which is equal to 0.005 m^2) can be calculated as:
Energy received = (1 KJ m^-2 s^-1) * (0.005 m^2) * (600 s)
Energy received = 3 KJ
Step 2: Determine the energy required to vaporize ethanol.
To vaporize ethanol, we need to know its specific heat of vaporization. Ethanol has a heat of vaporization of approximately 38.56 kJ/mol.
The molar mass of ethanol (C2H5OH) is:
(2 * atomic mass of carbon) + (6 * atomic mass of hydrogen) + atomic mass of oxygen
= (2 * 12.01 g/mol) + (6 * 1.008 g/mol) + 16.00 g/mol
= 46.07 g/mol
To calculate the energy required to vaporize ethanol per gram, we divide the heat of vaporization by the molar mass:
Energy required per gram = (38.56 kJ/mol) / (46.07 g/mol)
Energy required per gram = 0.837 kJ/g
Step 3: Calculate the maximum mass of ethanol vaporized.
To determine the maximum mass of ethanol that can be vaporized, we divide the energy received from the sun in 10 minutes by the energy required per gram:
Maximum mass of ethanol vaporized = (Energy received) / (Energy required per gram)
Maximum mass of ethanol vaporized = 3 KJ / 0.837 kJ/g
Maximum mass of ethanol vaporized ≈ 3.58 grams
Therefore, the maximum mass of pure ethanol that can be vaporized in 10 minutes is approximately 3.58 grams.