The following reaction can be used to determine the amount of calcium ion present in milk. Before the reaction below is carried out ca2+ is precipitated out of a sample of milk as CaC2O4(s). The CaC2O4(s) is then titrated with MnO4-.
2MnO4-(aq) + 5CaC2O4(s) + 16H+(aq) = 2Mn2+(aq) + 5Ca2+(aq) + 10CO2(g) + 8H2O(l)
(delta H) = -1535 kJ
A quantity of CaC2O4(s) is obtained by precipitating Ca2+ from a 660.-ml sample of milk. It takes 34.0 ml of 0.225 M MnO4- to titrate the CaC2O4.
a. How many moles of MnO4- were used in the titration?
b. what is the concentration (molarity) of Ca2+ in the milk sample?
c. how much heat, in kJ, was given off by the reaction during the titration?
d. If the titration was performed at 0 C and 1 atm of pressure, what volume of CO2 was produced during the titration?
IF you could help me by answering and showing how you did it (equations) that would be great.
Thanks.
The following reaction can be used to determine the amount of calcium ion present in milk. Before the reaction below is carried out ca2+ is precipitated out of a sample of milk as CaC2O4(s). The CaC2O4(s) is then titrated with MnO4-.
2MnO4-(aq) + 5CaC2O4(s) + 16H+(aq) = 2Mn2+(aq) + 5Ca2+(aq) + 10CO2(g) + 8H2O(l)
(delta H) = -1535 kJ
A quantity of CaC2O4(s) is obtained by precipitating Ca2+ from a 660.-ml sample of milk. It takes 34.0 ml of 0.225 M MnO4- to titrate the CaC2O4.
a. How many moles of MnO4- were used in the titration?
mols MnO4^- = M x L
b. what is the concentration (molarity) of Ca2+ in the milk sample?
Use the coefficients in the balanced equation to convert moles MnO4^- to moles Ca^+2.
moles Ca^+2 = moles MnO4^- x (5 moles CaC2O4/2MnO4^-) = ??moles MnO4^- x (5/2) = xx moles Ca^+2
Then molarity Ca^+2 = xx moles Ca^+2/0.660L
c. how much heat, in kJ, was given off by the reaction during the titration? Is that 1535 kJ for the reaction? If so, then (1535 kJ/5 mole) x (xx moles CaC2O4) = ??
d. If the titration was performed at 0 C and 1 atm of pressure, what volume of CO2 was produced during the titration?
Convert moles MnO4^- to moles CO2 (the same process used in the part b above), then use PV = nRT to calculate volume OR the simpler way is to recognize that OC and 1 atm is STP and you know 1 mole of a gas occupies 22.4L at STP; therefore, moles CO2 x 22.4 = volume (in liters) of CO2 gas.
Sure! Let's go through each question step by step:
a. To determine the number of moles of MnO4- used in the titration, we can use the equation:
2MnO4-(aq) + 5CaC2O4(s) + 16H+(aq) -> 2Mn2+(aq) + 5Ca2+(aq) + 10CO2(g) + 8H2O(l)
The balanced equation tells us that 2 moles of MnO4- react with 5 moles of CaC2O4. From the information given, we know that 34.0 mL of 0.225 M MnO4- was used.
First, we need to convert the volume from mL to L:
34.0 mL = 34.0 mL * (1 L / 1000 mL) = 0.034 L
Now, we can calculate the number of moles of MnO4- used:
moles of MnO4- = volume (L) * concentration (M)
moles of MnO4- = 0.034 L * 0.225 M = 0.00765 moles
Therefore, 0.00765 moles of MnO4- were used in the titration.
b. To find the concentration (molarity) of Ca2+ in the milk sample, we can use the stoichiometry from the balanced equation. From the equation, we know that 5 moles of CaC2O4 react with 5 moles of Ca2+.
We need to convert the volume of MnO4- used (34.0 mL) to moles of CaC2O4:
moles of CaC2O4 = moles of MnO4- * (5 moles CaC2O4 / 2 moles MnO4-)
moles of CaC2O4 = 0.00765 moles * (5 moles CaC2O4 / 2 moles MnO4-) = 0.0191 moles
Now, let's calculate the concentration of Ca2+ in the milk sample:
concentration of Ca2+ = moles of Ca2+ / volume of milk (L)
concentration of Ca2+ = 0.0191 moles / 0.660 L = 0.0289 M
Therefore, the concentration of Ca2+ in the milk sample is 0.0289 M.
c. The enthalpy change (ΔH) of the reaction is -1535 kJ per mole of reaction. To calculate the heat given off during the titration, we can use the equation:
heat (kJ) = moles of reaction * ΔH
From part a, we know that 0.00765 moles of MnO4- were used in the reaction. Therefore:
heat (kJ) = 0.00765 moles * -1535 kJ/mol = -11.7 kJ
Therefore, the reaction gave off 11.7 kJ of heat during the titration.
d. To find the volume of CO2 produced during the titration, we can use the stoichiometry from the balanced equation. From the equation, we know that 5 moles of CaC2O4 produce 10 moles of CO2.
Using the moles of CaC2O4 calculated in part b (0.0191 moles), we can calculate the moles of CO2 produced:
moles of CO2 = moles of CaC2O4 * (10 moles CO2 / 5 moles CaC2O4)
moles of CO2 = 0.0191 moles * (10 moles CO2 / 5 moles CaC2O4) = 0.0382 moles
Finally, we can calculate the volume of CO2 using the ideal gas law:
V = (moles of CO2 * R * T) / P
Assuming the temperature (T) is 0°C (273 K) and pressure (P) is 1 atm, and using the ideal gas constant (R) of 0.08206 L·atm/(K·mol), we can calculate the volume:
V = (0.0382 moles * 0.08206 L·atm/(K·mol) * 273 K) / 1 atm
V = 0.866 L
Therefore, the volume of CO2 produced during the titration is 0.866 L.
I hope this helps! Let me know if you have any further questions.
Sure! I'd be happy to help you with these questions.
a. To find the number of moles of MnO4- used in the titration, we can use the given volume and molarity of the MnO4- solution. The equation shows that the stoichiometric ratio between MnO4- and CaC2O4 is 2:5. Therefore, we can set up the following equation:
(0.0340 L) x (0.225 mol/L) = moles of MnO4-
Using this equation, we find that the number of moles of MnO4- used in the titration is 0.00765 mol.
b. To find the concentration of Ca2+ in the milk sample, we can use the stoichiometric ratio between MnO4- and CaC2O4 from the balanced equation. The stoichiometric ratio suggests that 2 moles of MnO4- react with 5 moles of CaC2O4. Since we know the number of moles of MnO4- used in the titration (0.00765 mol), we can calculate the number of moles of CaC2O4:
moles of CaC2O4 = (5/2) x moles of MnO4-
= (5/2) x 0.00765 mol
= 0.0191 mol
Now, we need to convert moles of CaC2O4 to the concentration of Ca2+ in the milk sample. Since the volume of the milk sample is given as 660. mL (0.660 L), we can use the following formula:
concentration of Ca2+ = moles of CaC2O4 / volume of milk sample
concentration of Ca2+ = 0.0191 mol / 0.660 L
= 0.0289 M (rounded to four significant figures)
Therefore, the concentration of Ca2+ in the milk sample is 0.0289 M.
c. To find the amount of heat given off by the reaction during the titration, we need to use the enthalpy change (ΔH) given in the question, which is -1535 kJ. The stoichiometric ratio between CaC2O4 and heat is 5:1535 kJ. So, we can calculate the amount of heat released by using the formula:
heat released = (ΔH / 5) x moles of CaC2O4
heat released = (-1535 kJ / 5) x 0.0191 mol
= -587 kJ (rounded to three significant figures)
Therefore, the heat released by the reaction during the titration is -587 kJ.
d. To find the volume of CO2 produced during the titration, we need to consider the stoichiometric ratio between CaC2O4 and CO2 from the balanced equation, which is 5:10. Since we know the number of moles of CaC2O4 used in the titration (0.0191 mol), we can calculate the number of moles of CO2 produced:
moles of CO2 = (10/5) x moles of CaC2O4
= (10/5) x 0.0191 mol
= 0.0382 mol
Next, we can use the ideal gas law to calculate the volume of CO2 produced. Assuming the titration was performed at 0°C (273 K) and 1 atm of pressure, we can use the following formula:
V = (n x R x T) / P
V = (0.0382 mol) x (0.0821 L·atm/mol·K) x (273 K) / (1 atm)
= 0.859 L (rounded to three decimal places)
Therefore, the volume of CO2 produced during the titration is 0.859 L.
I hope this helps! Let me know if you have any further questions.