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A reaction requires 22.4 L of gas at STP. You have 45.0 L of gas at 100 kPa and 373 K. Which of the following statements is true? The gas constant is 8.31 L-kPa/mol-K.
You will have an excess of gas and the reaction will occur. <---------
You will have too much gas for the reaction to occur.
You do not have enough gas for the reaction to occur.
You cannot tell given this information.
You will have an excess of gas and the reaction will occur.
To determine if you have enough gas for the reaction to occur, we need to compare the molar amounts of gas at STP and the given conditions.
First, let's calculate the moles of gas you have at the given conditions (45.0 L, 100 kPa, and 373 K). We can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in kPa)
V = volume (in L)
n = moles
R = gas constant (8.31 L-kPa/mol-K)
T = temperature (in K)
Rearranging the equation to solve for n, we get:
n = PV / RT
Substituting the values into the equation:
n = (100 kPa)(45.0 L) / (8.31 L-kPa/mol-K)(373 K)
n ≈ 5.6 moles
Now, let's compare this to the molar amount of gas required for the reaction at STP. We know that 1 mole of gas occupies 22.4 L at STP. So, to find the number of moles required, we divide the volume given (22.4 L) by the molar volume:
n_required = 22.4 L / 22.4 L/mol
n_required = 1 mole
Comparing the moles of gas you have (5.6 moles) to the moles required (1 mole), it is clear that you have an excess of gas. Therefore, the correct statement is: "You will have an excess of gas and the reaction will occur."
To determine whether there is an excess or a deficiency of gas for the reaction to occur, we can compare the given volume and conditions of the gas to the volume of gas required at STP.
1. Convert the given volume of gas to the conditions at STP (Standard Temperature and Pressure):
Using 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 gas constant, and T is the temperature, we can rearrange the equation to solve for the number of moles:
n = PV / RT
Given:
P = 100 kPa
V = 45.0 L
R = 8.31 L-kPa/mol-K
T = 373 K
Calculate moles of gas:
n = (100 kPa * 45.0 L) / (8.31 L-kPa/mol-K * 373 K)
2. Convert moles of gas to the volume at STP:
Since the gas constant is given in liters (L), we can assume the volume of gas is directly proportional to the number of moles. Therefore, we can convert moles of gas to the volume at STP by using the expression:
Volume at STP = (n * 22.4 L) / moles at STP
Given the volume of gas at STP is 22.4 L, we can substitute the calculated moles into the equation to find the volume at STP.
3. Compare the volume at STP to the given volume:
- If the volume at STP is less than the given volume, it means we have an excess of gas and the reaction will occur.
- If the volume at STP is greater than the given volume, it means we have too much gas for the reaction to occur.
- If the volume at STP is equal to the given volume, it means we have exactly enough gas for the reaction to occur.
Now, calculate the moles of gas using the given values:
n = (100 kPa * 45.0 L) / (8.31 L-kPa/mol-K * 373 K)
n = 209.6274 mol
Next, calculate the volume at STP using the formula mentioned earlier:
Volume at STP = (n * 22.4 L) / moles at STP
Volume at STP = (209.6274 mol * 22.4 L) / 1 mol
Volume at STP = 4691.9536 L
Finally, compare the volume at STP (22.4 L) with the given volume (45.0 L):
Since the volume at STP is less than the given volume, we can conclude that there is an excess of gas and the reaction will occur.
Therefore, the correct statement is: "You will have an excess of gas and the reaction will occur."