To change 30% of the original sample of ice to steam and 70% to stay in liquid form, approximately 14,658,000 grams of gasoline would be needed. This involves calculating the amount of ice that stays in liquid form, the amount of heat required, and the amount of gasoline needed to provide the required heat.
To determine the grams of gasoline required to change 30% of the original sample of ice to steam and 70% to stay in liquid form, we need to follow these steps:
Calculate the amount of ice that stays in liquid form.
Determine the amount of heat required to change the ice to steam and back to liquid form.
Calculate the amount of gasoline needed to provide the required heat.
(a) Calculate the amount of ice that stays in liquid form:
30% of 3000 grams = 0.3 * 3000 = 900 grams
(b) Determine the amount of heat required:
The heat required to change 1 gram of ice to steam is 80 calories.
The heat required to change 900 grams of ice to steam = 80 * 900 = 720,000 calories
The heat required to change 900 grams of steam back to liquid form is the same as the heat required to change ice to steam, 720,000 calories.
(c) Calculate the amount of gasoline needed:
The heat released by the complete reaction of 0.400 mol of Cl2 with excess SO2 is -1.54 kcal/mol
The heat required to change 900 grams of ice to steam is 720,000 calories.
The heat released by the complete reaction of 0.400 mol of Cl2 with excess SO2 is -1.54 kcal/mol * 0.400 mol = 0.616 kcal.
The number of moles of gasoline needed = 720,000 calories / 0.616 kcal/mol = 1178,000 moles.
The grams of gasoline needed = 1178,000 moles * 122.01 g/mol = 14,658,000 grams.
Therefore, approximately 14,658,000 grams of gasoline would be required to change 30% of the original sample of ice to steam and 70% to stay in liquid form.