SO2 and O2 are placed in a 2.00 L container at a temperature of 786 °C and a pressure of 6.99 atm. During the reaction, SO3 forms and the pressure falls to 1.89 atm. Determine how many moles of SO3 are generated.
To determine the number of moles of SO3 generated, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin
The first step is to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 786 °C + 273.15
T(K) = 1059.15 K
Now, we can use the ideal gas law to find the number of moles before and after the reaction.
For the initial conditions:
P1 = 6.99 atm
V1 = 2.00 L
T1 = 1059.15 K
For the final conditions:
P2 = 1.89 atm
V2 = 2.00 L
T2 = 1059.15 K
Let's first calculate the number of moles of the starting gases (SO2 and O2) using the initial conditions:
n1 = (P1 * V1) / (R * T1)
= (6.99 atm * 2.00 L) / (0.0821 L·atm/mol·K * 1059.15 K)
n1 = 0.1316 moles
Next, we'll calculate the number of moles of SO3 formed:
n2 = (P2 * V2) / (R * T2)
= (1.89 atm * 2.00 L) / (0.0821 L·atm/mol·K * 1059.15 K)
n2 = 0.0453 moles
To determine the number of moles of SO3 generated, we can subtract the initial moles (n1) from the moles after the reaction (n2):
n_SO3_generated = n2 - n1
= 0.0453 moles - 0.1316 moles
n_SO3_generated = -0.0863 moles
The negative value suggests that more SO2 and O2 were consumed than formed SO3. This could be due to an incomplete reaction or other factors affecting the reaction.