Calculate the volume of methane produced by the breakdown of 3.19 kg of sugar at 250 K and 702 torr
To calculate the volume of methane produced by the breakdown of sugar, we need to use the ideal gas law equation, 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.
First, let's convert the given pressure of 702 torr to units of atm. Since 1 atm = 760 torr, we can divide 702 torr by 760 torr/atm to get the pressure in atm:
702 torr ÷ 760 torr/atm ≈ 0.922 atm
Next, we need to calculate the number of moles of methane produced. We can use the molar mass of methane to convert the mass of sugar to moles of sugar, and then use the balanced chemical equation for the breakdown of sugar to methane to find the mole ratio.
1 mol of sugar → 16 mol of methane (according to the balanced equation)
First, let's find the number of moles of sugar:
Molar mass of sugar (C12H22O11) = 342.3 g/mol
Mass of sugar = 3.19 kg = 3190 g
Number of moles of sugar = mass of sugar / molar mass of sugar
= 3190 g / 342.3 g/mol
≈ 9.32 mol
Now, using the mole ratio from the balanced equation, we can calculate the number of moles of methane produced:
Number of moles of methane = 9.32 mol × (16 mol of methane / 1 mol of sugar)
≈ 149 mol
Now we have all the required values to plug into the ideal gas law equation:
P = 0.922 atm (given)
V = ? (to be calculated)
n = 149 mol (calculated)
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
T = 250 K (given)
Rearranging the ideal gas law equation, we can solve for volume:
V = (nRT) / P
Substituting the given values:
V = (149 mol × 0.0821 L·atm/(mol·K) × 250 K) / 0.922 atm
Calculating,
V ≈ 3380 L
Therefore, approximately 3380 liters of methane will be produced by the breakdown of 3.19 kg of sugar at 250 K and 702 torr.