Consider the reaction below.
C3H8 + 5 O2 3 CO2 + 4 H2O
How many litres of CO2 will be produced when 10.0 L of O2 are completely
reacted with C3H8? Assume that the volumes of the reagents and products are
measured at constant pressure and temperature.
With all gases in the equation one may use a shortcut in which volumes are considered as mols.
Convert 10 L O2 to ? L CO2.
10 L O2 x (3 mols CO2/5 mols O2) = 10 x 3/5 = ? L CO2.
To find the volume of CO2 produced, we need to determine the stoichiometry of the reaction. From the balanced equation:
C3H8 + 5 O2 -> 3 CO2 + 4 H2O
We can see that for every 5 moles of O2, 3 moles of CO2 are produced. Therefore, the ratio is 3/5.
Given that 10.0 L of O2 is completely reacted, we can use this ratio to calculate the volume of CO2 produced.
Volume of CO2 = (Volume of O2 / (5 L O2 / 3 L CO2))
Volume of CO2 = (10.0 L O2 / (5 L O2 / 3 L CO2))
Volume of CO2 = 10.0 L O2 * (3 L CO2 / 5 L O2)
Volume of CO2 = 6 L CO2
Therefore, when 10.0 L of O2 are completely reacted with C3H8, 6.0 L of CO2 will be produced.
To find out how many liters of CO2 will be produced, we need to use the stoichiometry of the balanced chemical equation. The coefficients of the balanced equation tell us the mole ratio between the reactants and products.
In this case, the balanced equation is:
C3H8 + 5 O2 → 3 CO2 + 4 H2O
From the equation, we see that 1 mole of C3H8 reacts with 5 moles of O2 to produce 3 moles of CO2.
First, we need to convert the given volume of O2 (10.0 L) to moles. To do this, we use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas (which is constant in this case),
V is the volume of the gas,
n is the number of moles of the gas,
R is the ideal gas constant,
T is the temperature in Kelvin.
Assuming constant pressure and temperature, we can rearrange the equation to solve for n:
n = PV / RT
Now, we can calculate the number of moles of O2 using the given volume, pressure, and temperature. Let's assume the pressure is 1 atm and the temperature is 298 K (standard conditions):
n(O2) = (10.0 L) x (1 atm) / (0.0821 L·atm/(mol·K) x 298 K)
= 0.405 moles
According to the stoichiometry of the balanced equation, 5 moles of O2 reacts with 3 moles of CO2. Hence, we can determine how many moles of CO2 will be produced:
n(CO2) = (3 moles CO2 / 5 moles O2) x (0.405 moles O2)
= 0.243 moles CO2
Finally, we can convert the moles of CO2 to liters using the ideal gas law equation in reverse:
V = nRT / P
Assuming constant pressure, we can use the same pressure and temperature values from before:
V(CO2) = (0.243 moles) x (0.0821 L·atm/(mol·K) x 298 K) / (1 atm)
= 5.81 L
Therefore, when 10.0 L of O2 reacts with C3H8, it will produce approximately 5.81 L of CO2.