A typical bathtub can hold 93 gallons of
water. Calculate the mass of natural gas that would need to be burned to heat the water for a tub of this size from 60◦F to 99◦F. Assume that the natural gas is pure methane(CH4) and that the products of combustion are carbon dioxide and water (liquid).
Answer in units of g
Convert 93 gallons H2O to grams. I would use 1 gallon = 3.785 L, convert to mL then use density of 1.00 g/mL to solve for grams. How much heat is required to heat this much water (in grams) from 60 F to 99 F. Convert 60 F and 99 F to C using (F-32)*5/9 = C.
Then q = heat required = mass H2O x specific heat H2O (that's 4.184 J/g*C) x (Tfinal-Tinitial) with T in C (not in F)
Now that you know how much heat is required, you want to calculate the amount of CH4 needed to produce that heat. If you don't know the heat of combustion you can calculate it this way.
CH4 + 2O2 ==> CO2 + 2H2O
dHrxn = (n*dH products) - (n*dH reactants). That is about 891 kJ/mol CH4 (note H2O is a liquid here).
So you need 16g x (q from above/891)= ?g CH4.
This is a time burner. What do you not understand about this?
i don't know equation to use.
Okay. I did each of these steps and I didn't get the correct answer.
What volume of natural gas does this correspond to at 25◦C and 0.8 atm?
Answer in units of L
I could not find the answer to the question above but this question uses the answer to the other question. So can you please help me.
To calculate the mass of natural gas needed to heat the water in a bathtub, we can use the following steps:
1. Determine the change in temperature:
The change in temperature is the final temperature (99°F) minus the initial temperature (60°F):
Change in temperature = 99°F - 60°F = 39°F
2. Convert the temperature change to Celsius:
We need to convert the temperature change from Fahrenheit to Celsius:
Change in temperature (Celsius) = (39°F - 32) × 5/9 = 4.444°C
3. Calculate the heat energy required to raise the temperature:
The heat energy required to raise the temperature of a substance can be calculated using the specific heat capacity (C) formula:
Heat energy = mass × specific heat capacity × temperature change
In this case, we want to calculate the mass (m) of the natural gas. Since the specific heat capacity of natural gas is not provided, we can assume it is similar to methane (CH4).
The specific heat capacity of methane (CH4) is 2.22 J/g°C.
4. Calculate the mass of natural gas (CH4):
Rearranging the formula in step 3, we can solve for the mass:
mass = heat energy / (specific heat capacity × temperature change)
We know that the heat energy needed to raise the temperature of the water is the same as the heat released when burning the natural gas. The heat of combustion for methane (CH4) is approximately 55.5 kJ/g.
Converting the heat of combustion from kJ/g to J/g: 55.5 kJ/g = 55,500 J/g
Substituting the values into the formula:
mass = (55,500 J/g) / (2.22 J/g°C × 4.444°C)
Simplifying the equation:
mass = 55,500 J / 9.868 J
mass ≈ 5614.54 g
So, the mass of natural gas that would need to be burned is approximately 5614.54 grams (g).