To determine which change would likely cause the greatest increase in the rate of the given reaction:
[tex]\[ \text{C}_2\text{H}_4(g) + \text{H}_2(g) \rightarrow \text{C}_2\text{H}_6(g) \][/tex]
Consider the underlying principles that affect the rate of chemical reactions, particularly for reactions involving gases:
### 1. Effect of Temperature
- Increasing Temperature: When the temperature is increased, the molecules of the reactants gain more kinetic energy.
- This means they move faster.
- Faster-moving molecules collide more frequently and with greater energy, thereby increasing the chances of effective collisions that lead to the reaction.
- Decreasing Temperature: Conversely, lowering the temperature decreases the kinetic energy of the molecules, reducing the frequency and energy of collisions, thereby slowing down the reaction rate.
### 2. Effect of Pressure
- Increasing Pressure: For gas-phase reactions, increasing the pressure reduces the volume available for the gas molecules, effectively increasing their concentration.
- Higher concentration of reactants results in more frequent collisions, which can lead to an increased rate of reaction.
- Decreasing Pressure: Lowering the pressure has the opposite effect; it increases the volume and decreases the concentration of the gas molecules, leading to fewer collisions and thus, a slower reaction rate.
### Combining the Effects
Considering the above points, we can analyze each option:
1. Decrease Temperature and Decrease Pressure:
- Both these changes slow down the reaction by reducing kinetic energy and decreasing the frequency of collisions. This combination would significantly decrease the reaction rate.
2. Increase Temperature and Decrease Pressure:
- Increasing temperature boosts the reaction rate, but decreasing pressure reduces the frequency of collisions. These opposing effects would likely result in a moderate change, with the decrease in pressure somewhat offsetting the increase in reaction rate due to higher temperature.
3. Decrease Temperature and Increase Pressure:
- Lowering temperature reduces kinetic energy, slowing down the reaction, whereas increasing pressure increases the frequency of collisions. These changes also oppose each other, and the result might be moderate, with the increased pressure somewhat counteracting the effect of the lower temperature.
4. Increase Temperature and Increase Pressure:
- Increasing both temperature and pressure will synergistically enhance the reaction rate. Higher temperature increases the kinetic energy and maximum collision energy, while higher pressure increases collision frequency by reducing the volume and increasing concentration.
- This combination leads to the most significant increase in the rate of reaction due to both factors working in unison to favor more effective collisions.
### Conclusion
The change that would likely cause the greatest increase in the rate of the reaction is:
- Increase temperature and increase pressure
Therefore, the answer is:
[tex]\[ \boxed{4} \][/tex]
