How many grams of water could have its temperature raised from 25 ºC (room temperature) to 100 ºC (the boiling point of water) by the amount of energy released in the formation of 4.0 mol of H2 from hydrogen atoms? The bond energy of H2 is 435 kJ/mol. The specific heat of water is 4.184 J/g °C. Express your answer in scientific notation.
I thought I worked this a couple of days ago.
4H ==> 2H2
So 435 kJ/mol x 2 mol = 870 kJ.
870,000J = mass H2O x specific heat H2O x (Tfinal-Tinitial)
Plug and chug. Solve for mass H2O
To solve this problem, we need to first calculate the energy released in the formation of 4.0 mol of H2 from hydrogen atoms. Then we can use this energy to determine the mass of water that can be heated from 25 ºC to 100 ºC.
Step 1: Calculate the energy released in the formation of 4.0 mol of H2.
The bond energy of H2 is given as 435 kJ/mol. Therefore, the energy released in forming 4.0 mol of H2 is:
Energy released = bond energy * number of moles
Energy released = 435 kJ/mol * 4.0 mol
Now, let's convert kJ into J:
Energy released = (435 kJ/mol * 4.0 mol) * (1000 J/1 kJ) = 1.74 x 10^6 J
Step 2: Determine the mass of water that can be heated using this energy.
The specific heat of water is given as 4.184 J/g °C. This means that it takes 4.184 J to heat 1 gram of water by 1 °C.
We're given the initial temperature as 25 ºC and the final temperature as 100 ºC. So, the temperature change is:
Temperature change = final temperature - initial temperature
Temperature change = 100 ºC - 25 ºC = 75 ºC
Now, let's calculate the mass of water using the formula:
Energy = mass of water * specific heat * temperature change
Rearranging the formula to solve for mass of water:
Mass of water = Energy / (specific heat * temperature change)
Plugging in the values:
Mass of water = (1.74 x 10^6 J) / (4.184 J/g °C * 75 ºC)
Mass of water = 52622.48 g
So, the mass of water that can be heated from 25 ºC to 100 ºC using the given energy is 5.262 x 10^4 g.