58. When a vehicle is parked in the sunlight on a hot summer day, the temperature inside can approach 55°C. One company has patented a non-CFC propelled aerosol that can be sprayed inside a vehicle to reduce the temperature to 25°C within seconds. The spray contains a mixture of two liquids: 10% ethanol, C2H5OH, and 90% water by mass.

Question

58. When a vehicle is parked in the sunlight on a hot summer day, the temperature inside can approach 55°C. One company has patented a non-CFC propelled aerosol that can be sprayed inside a vehicle to reduce the temperature to 25°C within seconds. The spray contains a mixture of two liquids: 10% ethanol, C2H5OH, and 90% water by mass.

equation: C2H5OH + H2O = 2CO2 + 6H2
1.0 g of the aerosol is sprayed into a hot vehicle. How much heat (in kJ) can be absorbed due to vaporization of the aerosol? Note: ΔHvap of water = 44.0 kJ/mol and ΔHvap of ethanol = 38.56 kJ/mol

i used the deltaH = n(deltaHx)

Answer 1

To calculate the amount of heat absorbed due to the vaporization of the aerosol, you need to find the moles of ethanol and water in the spray, and then multiply them by their respective enthalpy of vaporization.

Let's start by calculating the moles of ethanol (C2H5OH) and water (H2O) in the spray:

1. Calculate the moles of ethanol:
- First, we need to find the molecular weight of ethanol (C2H5OH). The atomic weights are C = 12.01 g/mol, H = 1.01 g/mol, and O = 16.00 g/mol.
- The molecular weight of ethanol is (2 × 12.01) + (6 × 1.01) + 16.00 = 46.07 g/mol.
- Now, we can calculate the moles of ethanol in the spray using its percentage of mass. The spray contains 10% ethanol, so for 1.0 g of aerosol, we have (1.0 g) × (0.1) / (46.07 g/mol) = 0.0217 mol of ethanol.

2. Calculate the moles of water:
- Since the spray contains 90% water, the amount of water in the spray is (1.0 g) × (0.9) = 0.9 g.
- The molecular weight of water (H2O) is 18.02 g/mol.
- We can now calculate the moles of water in the spray: (0.9 g) / (18.02 g/mol) = 0.0499 mol of water.

Now that we have the moles of ethanol and water, we can calculate the amount of heat absorbed due to vaporization using the equation:

ΔH = n × ΔHvap

where ΔHvap is the enthalpy of vaporization.

1. For ethanol, ΔHvap = 38.56 kJ/mol.
The heat absorbed by ethanol = (0.0217 mol) × (38.56 kJ/mol) = 0.8365 kJ.

2. For water, ΔHvap = 44.0 kJ/mol.
The heat absorbed by water = (0.0499 mol) × (44.0 kJ/mol) = 2.1956 kJ.

Finally, we sum up the heat absorbed by both ethanol and water:
Heat absorbed = 0.8365 kJ + 2.1956 kJ = 3.0321 kJ.

Therefore, approximately 3.0321 kJ of heat can be absorbed due to the vaporization of the aerosol when 1.0 g is sprayed into a hot vehicle.