During an experiment, a student adds 1.23 g of CaO to 200.0 mL of 0.500 M HCl. The student observes a temperature increase of 5.10 °C. Assuming the solution\'s final volume is 200.0 mL, the density if 1.00 g/mL, and the heat capacity is 4.184 J/(g·°C), calculate the heat of the reaction, ΔHrxn.i know i need to use the equations q=mcdeltaT and delta H= q/n but i keep getting the wrong answer. also which one is the limiting reactant in the equation CaO(s) +2H+(aq)-->Ca^2+(aq)+H2(g)
MY WORK
Q=10*4.184*5.1=213.384
delta H=213.384/1.23=173.483
Where do you get the 10?
mass H2O = 200 g
sp.h. = 4.184
delta T = 5.10
CaO is the limiting reagent.
Where do you get the H2(g)? There is no H2 gas liberated.
CaO + 2HCl ==> CaCl2 + 2H2O
CaO + 2H^+ ==> H2O + Ca^2+
To calculate the heat of the reaction (ΔHrxn), you are on the right track using the equation q = mcdeltaT. However, there is a mistake in your calculation for ΔHrxn.
Here's the correct step-by-step calculation:
1. Calculate the moles of CaO:
Given mass of CaO = 1.23 g
Molar mass of CaO = 40.08 g/mol (from periodic table)
Moles of CaO = mass/molar mass = 1.23 g / 40.08 g/mol = 0.03069 mol (rounded to 5 decimal places)
2. Determine the limiting reactant:
The balanced equation is CaO(s) + 2H+(aq) → Ca^2+(aq) + H2(g)
From the equation, you can see that the stoichiometry is 1:2 for CaO:H+, so 1 mole of CaO reacts with 2 moles of H+.
Given that the concentration of HCl is 0.500 M and the volume is 200 mL (which is converted to 0.200 L):
Moles of H+ = concentration x volume = 0.500 mol/L x 0.200 L = 0.100 mol
Since the mole ratio of CaO:H+ is 1:2, and you have less moles of CaO (0.03069 mol) compared to moles of H+ (0.100 mol), CaO is the limiting reactant.
3. Calculate the heat released (q) using the equation q = mcdeltaT:
Given:
mass (m) = 10.00 g (density 1.00 g/mL x 10.00 mL)
specific heat (c) = 4.184 J/(g·°C)
deltaT = 5.10 °C
q = mcdeltaT = 10.00 g x 4.184 J/(g·°C) x 5.10 °C = 213.2832 J (rounded to 4 decimal places)
4. Calculate the heat of the reaction (ΔHrxn):
To determine ΔHrxn, you need to divide q by the number of moles of the limiting reactant:
ΔHrxn = q / moles of CaO = 213.2832 J / 0.03069 mol = 6948 J/mol (rounded to 4 decimal places)
So, the heat of the reaction (ΔHrxn) is approximately 6948 J/mol.
The limiting reactant in this reaction is CaO because it is consumed completely and there is an excess of HCl.
To calculate the heat of the reaction (ΔHrxn), you need to use the equation q = mcdeltaT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and deltaT is the change in temperature.
In this case, you have a 1.23 g sample of CaO reacting with 0.5 M HCl. We need to determine which reactant is the limiting reactant. The balanced equation is:
CaO(s) + 2H+(aq) → Ca^2+(aq) + H2(g)
The stoichiometry of the reaction shows that 1 mole of CaO reacts with 2 moles of H+ ions.
First, convert the volume of the HCl solution to moles:
0.500 M HCl means there are 0.500 moles of H+ ions per liter of solution. Since the volume is 200.0 mL (0.200 L), the number of moles of H+ ions is:
0.500 moles/L * 0.200 L = 0.100 moles of H+ ions
Since the stoichiometry shows that 1 mole of CaO reacts with 2 moles of H+ ions, the number of moles of CaO needed is also 0.100 moles.
Next, calculate the heat transferred using the q = mcdeltaT equation. Given that the mass (m) is 1.23 g, the specific heat capacity (c) is 4.184 J/(g·°C), and the temperature change (deltaT) is 5.10 °C:
q = (1.23 g) * (4.184 J/(g·°C)) * (5.10 °C)
q = 26.79 J
Finally, divide the heat transferred (q) by the number of moles of CaO:
ΔHrxn = q / n
ΔHrxn = 26.79 J / 0.100 moles
ΔHrxn = 267.9 J/mol or 267.9 kJ/mol (since 1 kJ = 1000 J)
Therefore, the heat of the reaction (ΔHrxn) is 267.9 J/mol or 267.9 kJ/mol.
To determine the limiting reactant, compare the molar ratio of CaO to H+ ions in the balanced equation. Since 1 mole of CaO reacts with 2 moles of H+ ions, and you have 0.100 moles of H+ ions, the maximum amount of CaO that can react is 0.050 moles. Since you have 0.100 moles of CaO, it is in excess, and the limiting reactant is HCl.