6.1.4 Calculating Gradients

What is a Gradient?

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The gradient of a graph tells us how steep a line is. When we talk about the rate of a chemical reaction, the gradient of the graph can help us figure out how quickly the reaction is happening at a specific point in time.

Why Calculate the Gradient?

By calculating the gradient of a curve on a rate graph, we can determine the rate of reaction at any particular moment during the reaction. This is especially useful because the rate of a reaction often changes as the reaction progresses.

How to Calculate the Gradient:

To calculate the gradient of a curve on a graph, you first need to draw a tangent. A tangent is a straight line that touches the curve at just one point and doesn't cross it.
Once you've drawn the tangent, you can use it to calculate the gradient.

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Steps to Calculate the Gradient:

Draw a Tangent: Choose the point on the curve where you want to find the rate of reaction. Draw a straight line (tangent) that just touches the curve at that point.
Find the Change in Amount:

Draw two vertical lines from the points where the tangent intersects the y-axis.
The difference between these two points on the y-axis gives you the change in the amount of substance (this could be in grams, cm³, or moles, depending on what you're measuring).

Find the Change in Time:

Draw two horizontal lines from the points where the tangent intersects the x-axis.
The difference between these two points on the x-axis gives you the change in time (usually measured in seconds).

Calculate the Gradient: Use the formula:

Gradient= \frac{Change in Amount}{Change in Time}

This gives you the rate of reaction at the point where the tangent touches the curve.

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Example of Using a Gradient: Imagine you have a graph showing the amount of gas produced in a reaction over time. If you draw a tangent at a specific time and find that the gas amount changes by 10 cm³ over 2 seconds, you calculate the gradient (rate of reaction) as:

Rate of Reaction= \frac{10cm^3}{2s}=5 cm³/s

This means that at that specific time, the reaction is producing gas at a rate of 5 cm³ per second.

Why Use Tangents?

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Tangents are important because they let us measure the rate of reaction at a specific moment, not just the average rate over the entire reaction. This helps us understand how the reaction speed changes over time.

Calculating Gradients Simplified Revision Notes for GCSE AQA Chemistry Combined Science

6.1.4 Calculating Gradients

What is a Gradient?

Why Calculate the Gradient?

How to Calculate the Gradient:

Why Use Tangents?

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