Ca(H2PO4)2 and NaHCO3 are ingredients of baking powder which react with each other to produce CO2, thereby causing dough or batter to rise:
Ca(H2PO4)2 (s) + NaHCO3 (s) ----->
CO2 (g) + H2O (g) + CaHPO4 (s) + Na2HPO4 (s) (unbalanced)
If the baking powder contains 39 % NaHCO3 and 51 % Ca(H2PO4)2 by mass,
What volume (in Litres) of CO2 is produced from 1.00 g baking powder, assuming that 1 mol of CO2 occupies 63.7 L at 177 oC (a typical baking temperature)?
1. Balance the equation.
2. Convert 1.00 g baking powder to g of each ingredient by multiplying by the percentage (converted of course to a decimal).
3. This is a limiting reagent problem (probably) so
a. Convert g Ca(H2PO4)2 to mols.
b. Convert g NaHCO3 to mols.
4. Convert mols Ca(H2PO4)2 to mols CO2. Also, convert mols NaHCO3 to mols CO2. If the two answers are the same then then is not a limiting reagent problem and you may use the number of mols CO2. If the two numbers are not the same, the smaller number is the correct number to use and that reagent is the limiting reagent.
5. Convert mols CO2 to liters using your conversion fator in the problem.
Post your work if you get stuck.
To find the volume of CO2 produced from 1.00 g of baking powder, we need to first determine the amount of each reactant present in the baking powder.
1. Calculate the mass of NaHCO3 and Ca(H2PO4)2 in 1.00 g of baking powder:
- 39% of 1.00 g = 0.39 g NaHCO3
- 51% of 1.00 g = 0.51 g Ca(H2PO4)2
2. Convert the mass of each substance to the number of moles:
- Moles of NaHCO3 = (0.39 g NaHCO3) / (molar mass of NaHCO3)
- Similarly, calculate moles of Ca(H2PO4)2
3. Since the balanced equation gives the ratio of the reactants and products, we need to determine which reactant is limiting. Compare the moles of NaHCO3 and Ca(H2PO4)2 obtained in step 2 and choose the one with the lower number of moles. This reactant will be completely consumed in the reaction, and the other reactant will be in excess.
4. Use the stoichiometry of the balanced equation to find the moles of CO2 produced. The balanced equation shows that 1 mole of Ca(H2PO4)2 reacts to produce 1 mole of CO2.
5. Finally, use the ideal gas law to convert moles of CO2 to volume:
- PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
- Rearrange the equation to solve for V:
V = nRT / P
- n is the number of moles of CO2 calculated in step 4.
- R is the ideal gas constant (0.0821 L·atm/(mol·K)).
- P is the pressure, which is not provided. However, we have the volume of CO2 at a specific temperature mentioned in the question.
- Solve for V using the ideal gas law equation.
Following these steps, we can calculate the volume of CO2 produced from 1.00 g of baking powder.