Question

A) In the combustion of heptane, C7H16, carbon dioxide, CO2, is produced. Suppose that you want to collect 59.4 kg of CO2. What volume of heptane gas at 129.0°C must be burned at a pressure of 29.8 inHg to produce the CO2? Use R = 0.082057 L atm/mol K and Kelvin = 273.15 + °C. The molar mass of carbon dioxide is 44.01 g/mol. 29.92 inHg = 1 atm.

C7H16 (g) + 11 O2(g) → 7CO2(g) + 8H2O (g)

Answer 1

The volume of heptane gas that needs to be burned is 3.77 L. This can be calculated using the ideal gas law. The equation is PV = nRT, where P is the pressure (1 atm), V is the volume, n is the number of moles of heptane, R is the universal gas constant (0.082057 L atm/mol K) and T is the temperature in Kelvin (K = 273.15 + 129.0 = 402.15). To find the number of moles of heptane, we divide the mass of CO2 (59.4 kg) by its molar mass (44.01 g/mol). This gives us 1.34 mol of CO2. Since the equation is 7CO2 = C7H16, then 1.34 mol of CO2 is equivalent to 0.19 mol of heptane. Then, we plug the values into the ideal gas law equation and solve for V:

V = (0.19 mol)(0.082057 L atm/mol K)(402.15 K) / (1 atm)

V = 3.77 L

Answer 2

Step-by-step explanation:

First, we need to find the moles of CO2 that will be produced by using the given mass:

59.4 kg CO2 = 59400 g CO2

moles CO2 = 59400 g / 44.01 g/mol = 1349.2 mol CO2

According to the balanced chemical equation, 1 mole of heptane produces 7 moles of CO2. Therefore, the moles of heptane required can be calculated as:

moles heptane = moles CO2 / 7 = 1349.2 mol / 7 = 192.74 mol

Next, we can use the ideal gas law to calculate the volume of heptane gas at the given conditions:

PV = nRT

where P = 29.8 inHg = 1.011 atm (converted using 1 atm = 29.92 inHg), V is the volume we want to find, n = 192.74 mol, R = 0.082057 L atm/mol K, and T = 129.0°C = 402.15 K (converted using Kelvin = Celsius + 273.15).

Solving for V, we get:

V = nRT / P = (192.74 mol)(0.082057 L atm/mol K)(402.15 K) / 1.011 atm = 6573 L

Therefore, the volume of heptane gas required is 6573 L at the given conditions.