Question

Phosphate baking powder is a mixture of starch, sodium hydrogen carbonate, and cal- cium dihydrogen phosphate. When mixed with water, phosphate baking power releases carbon dioxide gas, causing a dough or batter to bubble and rise.

2 NaHCO3(aq) + Ca(H2PO4)2(aq) → Na2HPO4(aq) + CaHPO4(aq)
+2 CO2(g) + 2 H2O(l) If 2.2 L of CO2 is needed for a cake and each kilogram of baking power contains 168 g of NaHCO3, how much baking powder must be used to generate this amount of CO2? The density of CO2 at baking temperature is about
1.20 g/L.
Answer in units of g.

Answer 1

The balanced chemical equation for the reaction of NaHCO3 and Ca(H2PO4)2 is:

2 NaHCO3(aq) + Ca(H2PO4)2(aq) → Na2HPO4(aq) + CaHPO4(aq) + 2 CO2(g) + 2 H2O(l)

From the equation, we see that 2 moles of NaHCO3 produce 2 moles of CO2. Therefore, 1 mole of NaHCO3 produces 1 mole of CO2. We can use the molar mass of NaHCO3 to convert from moles to grams.

The molar mass of NaHCO3 is:

Na: 1 x 22.99 g/mol = 22.99 g/mol

H: 1 x 1.01 g/mol = 1.01 g/mol

C: 1 x 12.01 g/mol = 12.01 g/mol

O: 3 x 16.00 g/mol = 48.00 g/mol

Total molar mass = 22.99 + 1.01 + 12.01 + 48.00 = 83.01 g/mol

One kilogram (1000 g) of baking powder contains 168 g of NaHCO3. Therefore, one kilogram of baking powder contains:

1000 g baking powder × (168 g NaHCO3 / 1000 g baking powder) = 168 g NaHCO3

To produce 2.2 L of CO2 at baking temperature, we need:

2.2 L CO2 × (1.20 g CO2 / 1 L CO2) = 2.64 g CO2

Since 1 mole of NaHCO3 produces 1 mole of CO2, we need 2.64 g of NaHCO3 to produce 2.64 g of CO2. This corresponds to:

2.64 g NaHCO3 × (1 mol NaHCO3 / 83.01 g NaHCO3) × (1 kg baking powder / 168 g NaHCO3) = 0.0198 kg baking powder

Therefore, we need 0.0198 kg, or 19.8 g, of baking powder to generate 2.2 L of CO2 at baking temperature.

Step-by-step explanation: