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A reaction requires 22.4 L of gas at STP. There are 25.0 L of gas at 101.5 kPa and 373 K.

Which statement is true? Use the ideal gas law: PV = nRT where R = 8.31 L·kPa / mol·K

A. Given this information, there is no way to tell if there is enough gas for the reaction.
B. There is not enough gas for the reaction.
C. There is enough gas for the reaction.
D. There is excess gas for the reaction.

Sagot :

GinnyAnswer
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.
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