What is the zero order rate law?
2 Answers
The **zero-order rate law** describes a reaction where the rate is independent of the concentration of the reactants. In other words, the reaction rate remains constant and does not change as the concentration of the reactant decreases over time. This behavior is relatively uncommon, but it can occur under certain conditions, often in reactions where a catalyst or surface plays a key role in controlling the reaction rate.
### General Form of Zero-Order Rate Law:
The rate of a reaction is given by:
\[
\text{Rate} = k
\]
Where:
- \( k \) is the **rate constant** for the reaction.
- The rate is independent of the concentration of reactants, meaning even if you increase or decrease the amount of reactant, the rate remains the same as long as other conditions (like temperature and catalyst presence) are unchanged.
### Integrated Zero-Order Rate Law:
Over time, the concentration of a reactant decreases. For a zero-order reaction, the relationship between the concentration of reactants \([A]\) and time \(t\) can be described by the integrated form of the rate law:
\[
[A] = [A]_0 - kt
\]
Where:
- \([A]\) is the concentration of the reactant at time \(t\).
- \([A]_0\) is the **initial concentration** of the reactant.
- \(k\) is the rate constant.
- \(t\) is the time.
### Characteristics of Zero-Order Reactions:
1. **Rate is Constant**: In a zero-order reaction, the rate of the reaction is constant and independent of the concentration of the reactant.
2. **Linear Decrease in Concentration**: The concentration of the reactant decreases linearly over time. This is evident from the integrated rate law \([A] = [A]_0 - kt\), which shows that as time increases, the concentration of \([A]\) decreases in a straight line.
3. **Graphical Representation**: If you plot the concentration of the reactant \([A]\) versus time \(t\), you get a straight line with a slope of \(-k\). The y-intercept of the graph is the initial concentration \([A]_0\).
4. **Half-Life**: The half-life of a zero-order reaction is not constant and depends on the initial concentration of the reactant. It can be calculated using the formula:
\[
t_{1/2} = \frac{[A]_0}{2k}
\]
This means the half-life decreases as the concentration of the reactant decreases.
### Examples of Zero-Order Reactions:
- **Enzyme-Catalyzed Reactions**: When an enzyme is fully saturated with substrate, adding more substrate won't increase the reaction rate because the enzyme is already working at its maximum capacity.
- **Photochemical Reactions**: In some cases, reactions driven by light (such as photodegradation) can be zero-order because the rate depends on the intensity of light rather than the concentration of the reactant.
### Key Points to Remember:
- The rate of a zero-order reaction is constant.
- The concentration of the reactant decreases linearly with time.
- The rate is independent of the concentration of reactants.
- The half-life of a zero-order reaction decreases as the concentration decreases.
This is in contrast to **first-order** and **second-order** reactions, where the rate depends on the concentration of the reactant(s).
### General Form of Zero-Order Rate Law:
The rate of a reaction is given by:
\[
\text{Rate} = k
\]
Where:
- \( k \) is the **rate constant** for the reaction.
- The rate is independent of the concentration of reactants, meaning even if you increase or decrease the amount of reactant, the rate remains the same as long as other conditions (like temperature and catalyst presence) are unchanged.
### Integrated Zero-Order Rate Law:
Over time, the concentration of a reactant decreases. For a zero-order reaction, the relationship between the concentration of reactants \([A]\) and time \(t\) can be described by the integrated form of the rate law:
\[
[A] = [A]_0 - kt
\]
Where:
- \([A]\) is the concentration of the reactant at time \(t\).
- \([A]_0\) is the **initial concentration** of the reactant.
- \(k\) is the rate constant.
- \(t\) is the time.
### Characteristics of Zero-Order Reactions:
1. **Rate is Constant**: In a zero-order reaction, the rate of the reaction is constant and independent of the concentration of the reactant.
2. **Linear Decrease in Concentration**: The concentration of the reactant decreases linearly over time. This is evident from the integrated rate law \([A] = [A]_0 - kt\), which shows that as time increases, the concentration of \([A]\) decreases in a straight line.
3. **Graphical Representation**: If you plot the concentration of the reactant \([A]\) versus time \(t\), you get a straight line with a slope of \(-k\). The y-intercept of the graph is the initial concentration \([A]_0\).
4. **Half-Life**: The half-life of a zero-order reaction is not constant and depends on the initial concentration of the reactant. It can be calculated using the formula:
\[
t_{1/2} = \frac{[A]_0}{2k}
\]
This means the half-life decreases as the concentration of the reactant decreases.
### Examples of Zero-Order Reactions:
- **Enzyme-Catalyzed Reactions**: When an enzyme is fully saturated with substrate, adding more substrate won't increase the reaction rate because the enzyme is already working at its maximum capacity.
- **Photochemical Reactions**: In some cases, reactions driven by light (such as photodegradation) can be zero-order because the rate depends on the intensity of light rather than the concentration of the reactant.
### Key Points to Remember:
- The rate of a zero-order reaction is constant.
- The concentration of the reactant decreases linearly with time.
- The rate is independent of the concentration of reactants.
- The half-life of a zero-order reaction decreases as the concentration decreases.
This is in contrast to **first-order** and **second-order** reactions, where the rate depends on the concentration of the reactant(s).
To apply Ohm's Law, the circuit must satisfy two key conditions:
1. **Constant Temperature**: The temperature of the conductor should remain constant, as resistance can change with temperature variations.
2. **Ohmic Material**: The material of the conductor should be ohmic, meaning its resistance remains constant over the range of voltages and currents applied.
These conditions ensure that the relationship \( V = IR \) (voltage = current × resistance) holds true.
1. **Constant Temperature**: The temperature of the conductor should remain constant, as resistance can change with temperature variations.
2. **Ohmic Material**: The material of the conductor should be ohmic, meaning its resistance remains constant over the range of voltages and currents applied.
These conditions ensure that the relationship \( V = IR \) (voltage = current × resistance) holds true.