Answer :
To determine whether the given amount of gas is sufficient for the reaction, let's use the Ideal Gas Law, which is stated as [tex]\( PV = nRT \)[/tex].
Step 1: Calculate the number of moles required at standard temperature and pressure (STP).
Given:
- Volume required [tex]\( V_{\text{necessary}} = 22.4 \, \text{L} \)[/tex]
- Standard pressure [tex]\( P_{\text{STP}} = 101.3 \, \text{kPa} \)[/tex] (standard pressure)
- Standard temperature [tex]\( T_{\text{STP}} = 273.15 \, \text{K} \)[/tex]
- Ideal gas constant [tex]\( R = 8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K} \)[/tex]
Using the Ideal Gas Law:
[tex]\[ n_{\text{necessary}} = \frac{P_{\text{STP}} \cdot V_{\text{necessary}}}{R \cdot T_{\text{STP}}} \][/tex]
Let's plug in the values:
[tex]\[ n_{\text{necessary}} = \frac{101.3 \, \text{kPa} \times 22.4 \, \text{L}}{8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K} \times 273.15 \, \text{K}} \][/tex]
Step 2: Calculate the number of moles available with the given conditions.
Given:
- Volume available [tex]\( V_{\text{available}} = 25.0 \, \text{L} \)[/tex]
- Pressure [tex]\( P = 101.5 \, \text{kPa} \)[/tex]
- Temperature [tex]\( T = 373.0 \, \text{K} \)[/tex]
Using the Ideal Gas Law:
[tex]\[ n_{\text{available}} = \frac{P \cdot V_{\text{available}}}{R \cdot T} \][/tex]
Let's plug in the values:
[tex]\[ n_{\text{available}} = \frac{101.5 \, \text{kPa} \times 25.0 \, \text{L}}{8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K} \times 373.0 \, \text{K}} \][/tex]
Step 3: Compare the number of moles available to the number of moles necessary.
If [tex]\( n_{\text{available}} > n_{\text{necessary}} \)[/tex], there is excess gas for the reaction.
If [tex]\( n_{\text{available}} = n_{\text{necessary}} \)[/tex], there is enough gas for the reaction.
If [tex]\( n_{\text{available}} < n_{\text{necessary}} \)[/tex], there is not enough gas for the reaction.
Conclusion:
Based on the calculations:
- [tex]\( n_{\text{available}} \)[/tex] results in fewer moles than [tex]\( n_{\text{necessary}} \)[/tex].
Therefore, there is not enough gas for the reaction.
The correct statement is:
There is not enough gas for the reaction.
Step 1: Calculate the number of moles required at standard temperature and pressure (STP).
Given:
- Volume required [tex]\( V_{\text{necessary}} = 22.4 \, \text{L} \)[/tex]
- Standard pressure [tex]\( P_{\text{STP}} = 101.3 \, \text{kPa} \)[/tex] (standard pressure)
- Standard temperature [tex]\( T_{\text{STP}} = 273.15 \, \text{K} \)[/tex]
- Ideal gas constant [tex]\( R = 8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K} \)[/tex]
Using the Ideal Gas Law:
[tex]\[ n_{\text{necessary}} = \frac{P_{\text{STP}} \cdot V_{\text{necessary}}}{R \cdot T_{\text{STP}}} \][/tex]
Let's plug in the values:
[tex]\[ n_{\text{necessary}} = \frac{101.3 \, \text{kPa} \times 22.4 \, \text{L}}{8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K} \times 273.15 \, \text{K}} \][/tex]
Step 2: Calculate the number of moles available with the given conditions.
Given:
- Volume available [tex]\( V_{\text{available}} = 25.0 \, \text{L} \)[/tex]
- Pressure [tex]\( P = 101.5 \, \text{kPa} \)[/tex]
- Temperature [tex]\( T = 373.0 \, \text{K} \)[/tex]
Using the Ideal Gas Law:
[tex]\[ n_{\text{available}} = \frac{P \cdot V_{\text{available}}}{R \cdot T} \][/tex]
Let's plug in the values:
[tex]\[ n_{\text{available}} = \frac{101.5 \, \text{kPa} \times 25.0 \, \text{L}}{8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K} \times 373.0 \, \text{K}} \][/tex]
Step 3: Compare the number of moles available to the number of moles necessary.
If [tex]\( n_{\text{available}} > n_{\text{necessary}} \)[/tex], there is excess gas for the reaction.
If [tex]\( n_{\text{available}} = n_{\text{necessary}} \)[/tex], there is enough gas for the reaction.
If [tex]\( n_{\text{available}} < n_{\text{necessary}} \)[/tex], there is not enough gas for the reaction.
Conclusion:
Based on the calculations:
- [tex]\( n_{\text{available}} \)[/tex] results in fewer moles than [tex]\( n_{\text{necessary}} \)[/tex].
Therefore, there is not enough gas for the reaction.
The correct statement is:
There is not enough gas for the reaction.
