assume that 0.50 L of carbon dioxide is required for a loaf of bread. what mass of glucose must be broken down by yeast to produce this volume of carbon dioxide? (density of carbon dioxide at baking temp. is 1.25 g/L.
To find the mass of glucose that must be broken down by yeast to produce 0.50 L of carbon dioxide, we need to consider the stoichiometry of the reaction and the density of carbon dioxide at baking temperature.
First, let's determine the mass of carbon dioxide in 0.50 L using the density information given. We can use the formula:
mass = volume x density
mass of carbon dioxide = 0.50 L x 1.25 g/L
mass of carbon dioxide = 0.625 g
Now, we need to consider the stoichiometry of the reaction which states that one mole of glucose yields one mole of carbon dioxide. The molar mass of carbon dioxide (CO2) is approximately 44 g/mol.
We can set up the following conversion:
0.625 g CO2 x (1 mol CO2 / 44 g CO2) x (1 mol glucose / 1 mol CO2) x (180.16 g glucose / 1 mol glucose)
Let's break down this conversion:
- We start with 0.625 g of CO2.
- Using the molar mass of CO2 (44 g/mol), we convert grams to moles of CO2.
- From the stoichiometry of the reaction, we know that one mole of glucose is equivalent to one mole of CO2.
- Finally, we use the molar mass of glucose (180.16 g/mol) to convert moles of glucose to grams.
Performing the calculation:
0.625 g CO2 x (1 mol CO2 / 44 g CO2) x (1 mol glucose / 1 mol CO2) x (180.16 g glucose / 1 mol glucose)
= 0.625 g CO2 x (180.16 g glucose / 44 g CO2)
≈ 2.54 g glucose
Therefore, approximately 2.54 grams of glucose must be broken down by yeast to produce 0.50 liters of carbon dioxide.