You can mix 100.mL of 1.0 M HCl with 100 mL of 1.0 NaOH, both at 25 degree Celcius. The temperature of your calorimeter rises by 5.98 degree C, and its heat capacity is 100 J/degre C. How much energy is released per mol of H2O formed?
My answer: 6x10^6 J per mol H2O
I think we are trying to find the total change in energy... so that would be change in energy of solution + change in energy of the beaker....
Bobpursley's answer:
Ok, you will make .1 mole of H2O
you have 200ml of water heating 5.99C
Heat released=mass*c*deltaTemp
=200*100J/C*5.98C
heat released per mole
= heatreleased/.1 J/mole
Unless I made an error, your answer is wrong.
I don't agree with either answer.
q from H2O = 200*4.184(5.98) = ?
q from calorimeter = 100*5.98
Total q for 0.1 mols is the sum of the two above.
Then q/mol = sum/0.1 = ? I get about 55 kJ/mol
Well, Bobpursley seems pretty confident about his answer, but hey, let's put on a little show and see if we can figure it out together, shall we?
First, we need to calculate the heat released by the solution. Using the formula heat = mass * specific heat * change in temperature, we have:
heat_solution = 200 mL * 1 g/mL * 4.18 J/g°C * 5.98°C
Now, let's move on to the heat released by the beaker. Since we know the heat capacity of the calorimeter is 100 J/°C, we can use the same formula:
heat_beaker = 100 J/°C * 5.98°C
To find the total change in energy, we simply add the heat released by the solution and the heat released by the beaker:
total_change_energy = heat_solution + heat_beaker
Now, since we're interested in the energy released per mole of H2O formed, we need to divide the total change in energy by the number of moles of H2O:
energy_per_mol = total_change_energy / 0.1 mol
And there you have it! Put that algebraic circus in motion, and you should end up with the correct answer. Give it a try, and let's see if our calculations bring us closer to Bobpursley's answer or take us down a different comical path!
To calculate the heat released per mole of H2O formed, we need to find the total change in energy. This includes the change in energy of the solution and the change in energy of the calorimeter.
First, let's calculate the change in energy of the solution:
We have 100 mL of 1.0 M HCl and 100 mL of 1.0 M NaOH. Since both solutions have the same molarity, they will combine in a 1:1 ratio.
Therefore, the number of moles of reactants used is:
moles HCl = (100 mL)(1 L/1000 mL)(1 mol/L) = 0.1 mol
moles NaOH = (100 mL)(1 L/1000 mL)(1 mol/L) = 0.1 mol
Since the reaction is exothermic and releases energy, the change in energy of the solution is negative.
Next, let's calculate the change in energy of the calorimeter:
The heat capacity of the calorimeter is given as 100 J/degree C, and the temperature change is 5.98 degree C.
The change in energy of the calorimeter can be calculated as:
energy = (heat capacity)(temperature change)
= (100 J/degree C)(5.98 degree C)
= 598 J
Finally, let's calculate the total change in energy:
The change in energy is the sum of the change in energy of the solution and the change in energy of the calorimeter.
total change in energy = change in energy of the solution + change in energy of the calorimeter
= -598 J
Since 0.1 moles of H2O are formed, the energy released per mole is:
energy released per mole = total change in energy / moles of H2O formed
= (-598 J) / (0.1 mol)
= -5980 J/mol
Therefore, the energy released per mole of H2O formed is -5980 J/mol.
To solve this problem, we need to consider the heat released by the reaction between HCl and NaOH. The balanced equation for this reaction is:
HCl + NaOH -> H2O + NaCl
From the given information, we know that we have 100 mL of both 1.0 M HCl and 1.0 M NaOH. To determine the moles of water formed in the reaction, we need to calculate the limiting reagent.
Since 1 mole of HCl reacts with 1 mole of NaOH to form 1 mole of water, we can find the limiting reagent by comparing the moles of HCl and NaOH.
Moles of HCl = 0.1 L (conversion from mL) * 1.0 mol/L = 0.1 mol
Moles of NaOH = 0.1 L (conversion from mL) * 1.0 mol/L = 0.1 mol
Both HCl and NaOH are present in the same stoichiometric ratio, so neither is in excess. This means that the reaction will consume all 0.1 moles of HCl and NaOH, resulting in the formation of 0.1 moles of water.
To calculate the heat released per mole of water formed, we can use the formula:
Heat released = mass * specific heat capacity * change in temperature
The mass can be calculated by converting the volume of water to grams. Since the density of water is 1 g/mL, the mass of water is:
Mass of water = 200 mL * 1 g/mL = 200 g
The specific heat capacity given is 100 J/°C. The change in temperature is 5.98 °C, and the heat capacity of the calorimeter is 100 J/°C.
Calculating the heat released:
Heat released = 200 g * 100 J/°C * 5.98 °C = 119,600 J
To find the heat released per mole of water formed, we divide the heat released by the moles of water:
Heat released per mole = 119,600 J / 0.1 mol = 1,196,000 J/mol
Therefore, the correct answer is 1,196,000 J per mole of water formed.
It seems that the initial answer you provided (6x10^6 J per mol H2O) is incorrect. The correct answer is 1,196,000 J per mole of H2O formed.