A reaction requires 22.4 L of gas at STP. You have 30.5 L of gas at 101.5 kPa and 373 K. Which of the following statements is true? (Use the ideal gas law: PV = nRT where R = 8.31 L-kPa/mol-K.)
You will have excess gas for the reaction.
You will have enough gas for the reaction.
You do not have enough gas for the reaction.
Given this information, you cannot tell if you have enough gas for the reaction.
To determine whether you have enough gas for the reaction, we need to compare the amount of gas you have with the amount required by the reaction.
First, let's convert the conditions of the gas you have to STP (Standard Temperature and Pressure).
We can 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 in Kelvin.
Since we have the values for P, V, and T, we can calculate the number of moles of gas you have.
Given:
Pressure (P) = 101.5 kPa
Volume (V) = 30.5 L
Temperature (T) = 373 K
Ideal Gas Constant (R) = 8.31 L-kPa/mol-K
Rearranging the ideal gas law equation, we have:
n = PV / RT
Substituting the given values:
n = (101.5 kPa) * (30.5 L) / (8.31 L-kPa/mol-K) * (373 K)
Now, we can calculate the number of moles of gas you have.
n = (31.0025 kPa⋅L) / (8.31 L-kPa/mol-K) * (373 K)
n ≈ 14.40 mol
Next, we compare the number of moles you have to the number of moles required for the reaction.
Given that the reaction requires 22.4 L of gas at STP, we can calculate the number of moles required using the ideal gas law equation:
n = PV / RT
Substituting the given values at STP:
Pressure (P) = 101.3 kPa (approximately equals atmospheric pressure)
Volume (V) = 22.4 L
Temperature (T) = 273 K (standard temperature)
n = (101.3 kPa) * (22.4 L) / (8.31 L-kPa/mol-K) * (273 K)
n ≈ 9.90 mol
Comparing the number of moles you have (14.40 mol) to the number of moles required by the reaction (9.90 mol), we can conclude that you have enough gas for the reaction.
Therefore, the statement "You will have enough gas for the reaction" is true.
To determine if you have enough gas for the reaction, we can 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 gas constant, and T is the temperature.
First, let's convert the pressure from 101.5 kPa to atm by dividing by 101.3 kPa/1 atm = 1 atm/101.3 kPa = 0.999 atm (approximately).
Next, let's convert the temperature from Celsius to Kelvin by adding 273 to 373 K = 373 + 273 = 646 K.
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
For the 30.5 L of gas at 0.999 atm and 646 K:
n = (0.999 atm)(30.5 L) / (8.31 L-kPa/mol-K)(646 K)
n = 37.45 mol (approximately)
Therefore, you have 37.45 moles of gas available.
Since 22.4 L of gas is required for the reaction at STP, which is 1 mole of gas, and you have 37.45 moles of gas available, it is clear that you have enough gas for the reaction.
Thus, the statement "You will have enough gas for the reaction." is true.