For the reaction:
2H+(aq) + CO3-2(aq) --> CO2(g) + H2O(l)
A. Calculate the deltaHºrxn for the reaction. Given deltaHºf for CO3-2(aq) = -677.1 kJ/mol.
B. Using the above reaction, what would be the final temperature of a coffee cup calorimeter when 0.104 mol of hydrochloric acid react with 0.104 mol of sodium carbonate when 0.512 pounds of the solution starts at 25.2ºC with a specific heat capacity of 4.11 cal/(g ºC)?
A. To calculate the deltaHºrxn for the reaction, you need to find the enthalpy change for the reaction.
The balanced equation for the reaction is:
2H+(aq) + CO3-2(aq) --> CO2(g) + H2O(l)
Since the deltaHºf for CO3-2(aq) is given as -677.1 kJ/mol, we can use this value to calculate the deltaHºrxn.
The deltaHºrxn can be calculated using the formula:
deltaHºrxn = (sum of deltaHºf(products)) - (sum of deltaHºf(reactants))
In this case, the reactants are 2H+(aq) and CO32-(aq), and the products are CO2(g) and H2O(l).
deltaHºrxn = [deltaHºf(CO2(g)) + deltaHºf(H2O(l))] - [deltaHºf(2H+(aq)) + deltaHºf(CO32-(aq))]
Now we substitute the respective values from the given data:
deltaHºrxn = [0 kJ/mol + 0 kJ/mol] - [0 kJ/mol + (-677.1 kJ/mol)]
deltaHºrxn = 0 - (-677.1) kJ/mol
deltaHºrxn = 677.1 kJ/mol
Therefore, the deltaHºrxn for the reaction is 677.1 kJ/mol.
B. To determine the final temperature of the coffee cup calorimeter, you can use the equation:
q = mcΔT
Where:
q = heat transferred
m = mass of the solution in grams
c = specific heat capacity of the solution
ΔT = change in temperature
First, convert the mass of the solution from pounds to grams:
0.512 pounds * (453.59 g/pound) = 232.89 g
Next, calculate the heat transferred using the equation:
q = (232.89 g)(4.11 cal/gºC)(Tfinal - 25.2ºC)
Since 1 cal = 4.184 J, we need to convert the heat transferred to joules:
q = (232.89 g)(4.11 cal/gºC)(Tfinal - 25.2ºC) * (4.184 J/cal)
Given that 1 kJ = 1000 J, we can convert the heat transferred to kJ:
q = (232.89 g)(4.11 cal/gºC)(Tfinal - 25.2ºC) * (4.184 J/cal) * (1 kJ/1000 J)
Now that we know the value of q, we can substitute it into the first equation and solve for Tfinal:
q = mcΔT
(232.89 g)(4.11 cal/gºC)(Tfinal - 25.2ºC) * (4.184 J/cal) * (1 kJ/1000 J) = q
Substitute the given values for q:
0.104 mol HCl * (677.1 kJ/mol) = q
Solve for Tfinal:
(232.89 g)(4.11 cal/gºC)(Tfinal - 25.2ºC) * (4.184 J/cal) * (1 kJ/1000 J) = 0.104 mol HCl * (677.1 kJ/mol)
Simplify and solve for Tfinal:
(232.89 g)(4.11 cal/gºC)(Tfinal - 25.2ºC) * 4.184 * 10^(-3) kJ/gºC = 70.6 kJ
Rearrange the equation to solve for Tfinal:
(Tfinal - 25.2ºC) = (70.6 kJ) / [(232.89 g)(4.11 cal/gºC) * 4.184 * 10^(-3) kJ/gºC]
Now solve for Tfinal:
Tfinal = (70.6 kJ) / [(232.89 g)(4.11 cal/gºC) * 4.184 * 10^(-3) kJ/gºC] + 25.2ºC
Calculate the value of Tfinal using the given values:
Tfinal = (70.6 kJ) / [(232.89 g)(4.11 cal/gºC) * 4.184 * 10^(-3) kJ/gºC] + 25.2ºC
After calculating this expression, you will find the final temperature of the coffee cup calorimeter.
A. To calculate the ΔHºrxn (enthalpy change) for the reaction, you need to use the standard enthalpy of formation (ΔHºf) values for the reactants and products. These values represent the enthalpy change when one mole of a substance is formed from its elements in their standard states.
In this case, the given ΔHºf for CO3-2(aq) is -677.1 kJ/mol.
To calculate ΔHºrxn, you need to sum the ΔHºf values of the products and subtract the sum of the ΔHºf values of the reactants.
Reactants:
2H+(aq) and CO3-2(aq)
Products:
CO2(g) and H2O(l)
ΔHºrxn = (ΔHºf of CO2 + ΔHºf of H2O) - (ΔHºf of 2H+ + ΔHºf of CO3-2)
You will need to look up the ΔHºf values for H+(aq), H2O(l), and CO2(g) in a reliable source, such as a chemistry textbook or database.
B. To determine the final temperature of a coffee cup calorimeter, you can use the equation:
q = m * c * ΔT
Where:
q = heat transfer (in calories or joules)
m = mass of the solution (in grams or pounds)
c = specific heat capacity (in cal/(g ºC) or J/(g ºC))
ΔT = change in temperature (in ºC)
First, convert the mass of the solution from pounds to grams.
Then, calculate the heat transfer (q) using the equation above.
q = (mass of the solution) * (specific heat capacity) * (ΔT)
Finally, rearrange the equation to solve for ΔT.
ΔT = q / (mass of the solution * specific heat capacity)
Substitute the known values into the equation:
- mass of the solution
- specific heat capacity
- q (calculate using the reaction stoichiometry and enthalpy change)
This will give you the change in temperature (ΔT). To find the final temperature, add the change in temperature to the initial temperature of 25.2ºC.