Graphing in A-Level Chemistry | A-Level化学中的作图

📚 Graphing in A-Level Chemistry | A-Level化学中的作图

Graphing is one of the most practical skills in A-Level chemistry. It allows you to visualise trends, determine rates, calculate activation energies and judge the accuracy of experimental data. In AQA examinations, graph questions often carry significant marks, and a poorly drawn graph can cost you a grade.

作图是 A-Level 化学中最实用的技能之一。它帮助你观察趋势、计算速率、求活化能，并判断实验数据的准确性。在 AQA 考试中，作图题往往占分很高，一张画得不好的图可能让你丢掉一个等级。

1. Choosing the Correct Axes | 选择合适的坐标轴

The independent variable (the one you control) is always plotted on the x-axis. The dependent variable (the one you measure) is always plotted on the y-axis. In chemistry, time is almost always the independent variable, so it appears on the x-axis.

自变量（你控制的变量）永远画在 x 轴上，因变量（你测量的变量）永远画在 y 轴上。在化学中，时间几乎总是自变量，因此出现在 x 轴上。

Label each axis with the quantity and its unit, separated by a slash, e.g. t / s or volume / cm³.
每个坐标轴都要标出物理量和单位，中间用斜杠分隔，例如 t / s 或 volume / cm³。
Choose a scale that is easy to read. Avoid scales that make reading values awkward, such as 3 squares = 1 unit.
选择易于读数的刻度，避免像 3 格等于 1 单位这样难读的刻度。
The plotted points should fill at least half of the graph paper in both directions.
数据点应在纵横两个方向至少占据图纸的一半以上。

2. Plotting Points Accurately | 精确描点

Use a sharp pencil and plot points as small crosses or small dots. The mark should be clearly visible but not so large that it obscures the position of the data. If you use a dot, surround it with a small circle to make it visible.

用削尖的铅笔描点，画成小的十字叉或小圆点。标记要清晰可见，但不能大到遮盖数据点的准确位置。如果画圆点，可以在外面加一个小圆圈使其更明显。

The plotted point should be accurate to within ± 0.5 of the smallest grid division.

描点应精确到最小格子的 ± 0.5 以内。

Do not draw a point over another point if two readings coincide; instead, place them side by side or use a different symbol. In AQA mark schemes, a mis-plotted point usually loses the mark for that point.

如果两个读数重合，不要把点叠在一起画，应并排画或用不同符号区分。在 AQA 评分标准中，一个点画错通常会失去该点的分数。

3. Drawing the Line of Best Fit | 绘制最佳拟合线

The line of best fit is a smooth curve or straight line that best represents the overall trend of the data. It does not have to pass through every point, and it should ignore anomalous points. There should be a balance of points above and below the line.

最佳拟合线是一条能最好地代表数据整体趋势的光滑曲线或直线。它不必穿过每一个点，应忽略异常点。线上方和下方的点应大致均衡分布。

Use a ruler for a straight line / 画直线时必须用直尺。
If a curve is expected, draw a smooth curve freehand, not a series of straight segments / 如果预期是曲线，应徒手画光滑曲线，而不是折线。
Do not force the line through the origin unless the data and theory require it / 除非理论和数据要求，否则不要强行让线通过原点。

When determining a gradient, choose two points on the line that are far apart and not original data points. Draw a large triangle on the graph and show your working clearly.

计算斜率时，要在直线上选取两个相距较远的点，且这两个点不应是原始数据点。在图上画出大三角形，并清晰展示计算过程。

4. Identifying and Handling Anomalous Points | 识别与处理异常点

An anomalous point is a value that does not fit the pattern of the other results. You should investigate possible experimental errors, but on a graph you simply ignore it when drawing the line of best fit. Do not try to make the line pass through the anomaly.

异常点是指不符合其他结果规律的数值。你应当探究可能的实验误差，但在作图时只需在绘制最佳拟合线时忽略它，不要试图让线穿过异常点。

In AQA practical assessments, you may be asked to identify an anomalous point on a graph. State its approximate coordinates and explain that it may have been caused by a reading error, mis-timed measurement, or a loss of product.

在 AQA 实验考核中，你可能被要求在图上识别异常点。应指出其大致坐标，并解释它可能是由读数误差、计时错误或产物损失导致的。

5. Error Bars and Reliability | 误差线与可靠性

An error bar indicates the uncertainty in a measurement. For a burette reading ± 0.05 cm³, the total uncertainty for a titre is ± 0.10 cm³ because two readings are taken. If the error bar is large relative to the spread of the data, the gradient is less reliable.

误差线表示测量的不确定度。对于滴定管读数 ± 0.05 cm³，一次滴定用量涉及两次读数，所以总不确定度为 ± 0.10 cm³。如果误差线相对于数据的离散程度较大，那么斜率就较不可靠。

Uncertainty in a titre = 2 × 0.05 = ± 0.10 cm³

滴定体积的不确定度 = 2 × 0.05 = ± 0.10 cm³

In AQA, you are not usually required to draw error bars on graphs in written exams, but you must understand how uncertainties affect the reliability of a gradient or an intercept.

在 AQA 笔试中，通常不要求你在图上画误差线，但你必须理解不确定度如何影响斜率或截距的可靠性。

6. Interpolation and Extrapolation | 内插与外推

Interpolation means reading a value from within the range of the measured data. This is generally considered reliable because you are using the line between known points. Extrapolation means extending the line beyond the measured range; this is much less reliable because the trend may change outside the range tested.

内插是指从测量数据范围内读取一个数值。这通常被认为是可靠的，因为你使用的是已知点之间的线。外推则是将线延伸到测量范围之外；这远不那么可靠，因为趋势在测试范围之外可能发生变化。

Interpolation example: finding the concentration at a given time within your data / 内插示例：在数据范围内求某时刻的浓度。
Extrapolation example: estimating the volume of gas at 0 minutes by extending the line back / 外推示例：将线反向延长估计 0 分钟时的气体体积。

When you extrapolate, use a dashed line to show that it is an extension beyond the experimental data. This is a common requirement in AQA rate-of-reaction questions.

外推时应用虚线表示这是超出实验数据的延伸。这是 AQA 反应速率题目中的常见要求。

7. Linearising Curved Relationships | 曲线的线性化

Many chemical relationships are not linear, but they can be transformed to give a straight-line graph. For a relationship such as rate = k [A]ⁿ, taking logarithms gives:

许多化学关系不是线性的，但可以通过变换得到直线图。对于关系式 rate = k [A]ⁿ，取对数得：

log(rate) = n log[A] + log k

This is in the form y = mx + c, so plotting log(rate) against log[A] gives a straight line with gradient n and intercept log k. Similarly, for an Arrhenius plot, plotting ln k against 1/T gives a straight line with gradient −Ea/R.

这符合 y = mx + c 的形式，因此以 log(rate) 对 log[A] 作图得到直线，斜率为 n，截距为 log k。类似地，对于阿伦尼乌斯作图，以 ln k 对 1/T 作图得到直线，斜率为 −Ea/R。

ln k = −Ea/R × 1/T + ln A

Be careful with which logarithm you use. AQA often uses natural logarithms (ln) for Arrhenius plots and log₁₀ for rate-concentration graphs unless stated otherwise.

注意使用哪种对数。AQA 通常对阿伦尼乌斯图使用自然对数 (ln)，对速率-浓度图使用常用对数 (log₁₀)，除非题目另有说明。

8. Concentration–Time Graphs | 浓度-时间图

A concentration–time graph shows how the concentration of a reactant or product changes over time. The gradient of the tangent at any point gives the rate of reaction at that time.

浓度-时间图显示反应物或产物浓度随时间的变化。任意一点切线的斜率即为该时刻的反应速率。

If the graph is a straight line with a negative gradient, the rate is constant / 如果图形为斜率不变的直线，则速率恒定。
If the graph curves downward, the rate decreases as reactant concentration falls / 如果图形向下弯曲，则速率随反应物浓度降低而减小。
For a zero-order reaction, [A] vs t is a straight line / 对于零级反应，[A] 对 t 成直线。
For a first-order reaction, a graph of ln[A] vs t is a straight line / 对于一级反应，ln[A] 对 t 成直线。

To find the rate at a particular time, draw a tangent to the curve at that point and calculate its gradient. Use a transparent ruler for the tangent, and extend it across the graph to maximise accuracy.

要求某时刻的速率，需在该点画切线并计算其斜率。使用透明直尺画切线，并使其延伸到图的较大范围以提高精度。

9. Rate–Concentration Graphs | 速率-浓度图

A rate-concentration graph plots the initial rate against the initial concentration. The shape of the graph identifies the order of reaction with respect to that reactant.

速率-浓度图以初始速率对初始浓度作图。图形的形状可确定该反应物的反应级数。

Shape of graph	Order
Horizontal straight line (rate unchanged)	Zero order
Straight line through the origin	First order
Curve through the origin (rate ∝ [A]²)	Second order

Remember that the order with respect to a reactant tells you how the rate is affected when the concentration of that reactant changes. Do not confuse the order with the stoichiometric coefficient in the balanced equation — they are only equal for elementary reactions.

记住，关于某反应物的级数告诉你该反应物浓度变化如何影响速率。不要把级数与配平方程式中的化学计量系数混淆——它们只有对于基元反应才相等。

10. Titration Curves | 滴定曲线

A titration curve plots pH against the volume of acid or alkali added. The key features are the starting pH, the equivalence point, and the buffer region. In AQA, you may be asked to sketch and interpret titration curves for strong/strong, weak/strong, and strong/weak acid-base titrations.

滴定曲线以 pH 对加入的酸或碱体积作图。关键特征包括起始 pH、等当点和缓冲区域。在 AQA 中，你可能会被要求绘制并解释强酸-强碱、弱酸-强碱、强酸-弱碱等滴定曲线。

Strong acid + strong base: equivalence point pH = 7 / 强酸+强碱：等当点 pH = 7。
Weak acid + strong base: equivalence point pH > 7 / 弱酸+强碱：等当点 pH > 7。
Strong acid + weak base: equivalence point pH < 7 / 强酸+弱碱：等当点 pH < 7。

When sketching, use a sharp rise in pH near the equivalence point. The exact volume at the equivalence point is found using the tangent method on pH curves, where the equivalence point is at the centre of the steepest region.

画草图时，等当点附近 pH 应出现陡峭上升。在 pH 曲线上，可用切线法找等当点：等当点位于最陡区域的中心。

11. Common Mistakes in Exam Graphs | 考试作图常见错误

AQA examiners frequently report the same graph-drawing errors. Avoiding these mistakes can gain you several marks.

AQA 考官经常报告相同的作图错误。避免这些错误可以为你赢得几分。

Missing labels or units on axes / 坐标轴缺少名称或单位。
Using dots instead of crosses and then erasing them, leaving a messy graph / 用圆点代替十字叉，之后又擦掉，留下凌乱的图纸。
Drawing a curve that is too angular — a best-fit curve must be smooth / 把曲线画得太生硬——最佳拟合曲线必须光滑。
Forgetting to use a dashed line for extrapolation / 外推时忘记使用虚线。
Calculating the gradient without showing the triangle or the chosen points / 计算斜率时不展示三角形或所选点。
Not using enough significant figures in the gradient, or using more than the data supports / 斜率有效数字不足，或使用超过数据支持的位数。

Always use a pencil for all graph work, and take a spare sharpener and ruler into the exam.

所有作图工作必须用铅笔，考试时带上备用的卷笔刀和直尺。

12. Worked Example: Finding the Rate Constant from a Graph | 例题：由作图求速率常数

Consider a first-order decomposition of hydrogen peroxide. The concentration of H₂O₂ is measured at various times. To find k, plot ln[H₂O₂] against t. The gradient of the line is −k.

考虑 H₂O₂ 的一级分解反应。在不同时间测定 H₂O₂ 的浓度。为求 k，以 ln[H₂O₂] 对 t 作图。直线的斜率即为 −k。

ln[H₂O₂] = −k t + ln[H₂O₂]₀

Suppose two points on the line are (t = 100 s, ln[H₂O₂] = −1.50) and (t = 500 s, ln[H₂O₂] = −2.70). Then:

假设直线上两点为 (t = 100 s, ln[H₂O₂] = −1.50) 和 (t = 500 s, ln[H₂O₂] = −2.70)。则：

gradient = (−2.70 − (−1.50)) / (500 − 100) = −1.20 / 400 = −3.0 × 10⁻³ s⁻¹

斜率 = (−2.70 − (−1.50)) / (500 − 100) = −1.20 / 400 = −3.0 × 10⁻³ s⁻¹

Therefore k = 3.0 × 10⁻³ s⁻¹. Always include the correct units when quoting a rate constant.

因此 k = 3.0 × 10⁻³ s⁻¹。给出速率常数时务必带上正确的单位。

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Graphing in A-Level Chemistry | A-Level化学中的作图