2. Sulfuric acid comes from the oxidation of sulfur. The stages of the reactions are given below:
S + O2 --> SO2 ∆H= -296.8 kj
SO2 + 1/2 O2 --> SO3 ∆H= -98.9 kj
SO3 + H2O --> H2SO4 ∆H= -130.0 kj
The typical plant produces 750 tons of H2SO4 per day. Calculate amount of heat produced by the plant per day.
3. Each of 2 front tires in the car is filled with a different gas. One tire contains 116 g of helium, another tire has 160 g of unknown gas. How many times heavier is a molecule of the unknown gas than an atom of helium?
4. Suppose you want to heat air in your house with methane (CH4). Assume your house has 275 m2 of floor area and that ceiling is 2.50 m from the floor. The air in the house has a molar specific heat capacity of 29.1 j/mol*K. Average molar mass of air is 28.9 g and the density of air at these temperatures is 1.22 g/L. How much of methane do you need to burn in order to heat the air in the house from 15.0 to 22.0 oC?
Producing 98 g (1 mol) H2SO4 requires 296.8 + 98.9 + 130.0 kJ = ? kJ.
Convert 750 tons to grams = x
Then
total kJ*(x/98) = kJ/day for 750 tons.
2. To calculate the amount of heat produced by the plant per day, you need to calculate the energy released in each step and then multiply it by the number of moles of sulfuric acid produced.
Step 1: S + O2 -> SO2 (ΔH = -296.8 kJ)
Step 2: SO2 + 1/2 O2 -> SO3 (ΔH = -98.9 kJ)
Step 3: SO3 + H2O -> H2SO4 (ΔH = -130.0 kJ)
First, let's calculate the moles of sulfuric acid produced per day. Assuming the molar mass of H2SO4 is 98.09 g/mol:
750 tons = 750,000 kg = 750,000,000 g
moles of H2SO4 = 750,000,000 g / 98.09 g/mol ≈ 7,645,296 mol
Now, calculate the energy released in each step:
Step 1: -296.8 kJ/mol * 7,645,296 mol ≈ -2,267,174,069 kJ
Step 2: -98.9 kJ/mol * 7,645,296 mol ≈ -757,116,774 kJ
Step 3: -130.0 kJ/mol * 7,645,296 mol ≈ -995,186,880 kJ
Finally, add up the energy released in each step:
-2,267,174,069 kJ + (-757,116,774 kJ) + (-995,186,880 kJ) ≈ -4,019,477,723 kJ
So, the plant produces approximately -4,019,477,723 kJ of heat per day.
3. To find the number of times heavier the unknown gas molecule is compared to a helium atom, you need to calculate the molar mass of the unknown gas.
The molar mass of helium (He) is approximately 4.00 g/mol.
Given:
Mass of helium (He) = 116 g
Mass of unknown gas = 160 g
To find the molar mass of the unknown gas, divide its mass by the number of moles:
Molar mass of unknown gas = Mass of unknown gas / Moles of unknown gas
Moles of helium = Mass of helium / Molar mass of helium
Moles of helium = 116 g / 4.00 g/mol ≈ 29 mol
Now, divide the mass of the unknown gas by the moles of the unknown gas:
Moles of unknown gas = Mass of unknown gas / Molar mass of unknown gas
Solving for the molar mass of the unknown gas:
Molar mass of unknown gas = Mass of unknown gas / Moles of unknown gas
Molar mass of unknown gas = 160 g / (29 mol) ≈ 5.52 g/mol
To find how many times heavier the unknown gas molecule is compared to a helium atom, divide the molar mass of the unknown gas by the molar mass of helium:
Times heavier = Molar mass of unknown gas / Molar mass of helium
Times heavier = 5.52 g/mol / 4.00 g/mol ≈ 1.38
Therefore, the unknown gas molecule is approximately 1.38 times heavier than a helium atom.
4. To calculate the amount of methane (CH4) needed to heat the air in the house from 15.0 to 22.0 °C, you can use the equation:
q = (m * C * ΔT) / n
where:
q is the amount of heat needed (in joules),
m is the mass of air (in grams),
C is the molar specific heat capacity of air (in joules per mole per Kelvin),
ΔT is the change in temperature (in Kelvin), and
n is the molar mass of air (in grams per mole).
Given:
Floor area = 275 m^2
Ceiling height = 2.50 m
Specific heat capacity of air = 29.1 J/mol*K
Molar mass of air = 28.9 g/mol
Density of air = 1.22 g/L
First, calculate the volume of the house:
Volume = Floor area * Ceiling height
Volume = 275 m^2 * 2.50 m = 687.5 m^3
Convert volume to liters:
Volume = 687.5 m^3 * 1000 L/1 m^3 = 687,500 L
Now, calculate the mass of air in the house using the given density:
Mass of air = Volume * Density
Mass of air = 687,500 L * 1.22 g/L = 839,750 g
Convert mass of air to moles:
Moles of air = Mass of air / Molar mass of air
Moles of air = 839,750 g / 28.9 g/mol ≈ 29,034 mol
Calculate the change in temperature:
ΔT =