📚 Uncertainties | 不确定度
Measurement uncertainties are a core part of quantitative chemistry. In AQA A-level Chemistry, you must be able to estimate uncertainties for individual readings, combine them during calculations, and judge whether a result is reliable enough to support a conclusion.
测量不确定度是定量化学的核心内容。在 AQA A-level 化学中，你必须能够估计单次读数的不确定度、在计算过程中合成不确定度，并判断一个结果是否足够可靠以支持结论。
1. What Is an Uncertainty? | 什么是不确定度？
Every measurement has an uncertainty because no instrument can give an infinitely precise value. The uncertainty is the range within which the true value is expected to lie.
每次测量都有不确定度，因为没有仪器能给出无限精确的数值。不确定度是预期真实值所在的范围。
expressed as an absolute value, such as ±0.05 cm³, or as a percentage of the measurement.
不确定度并不意味着错误；它是测量过程的自然限制。它可以表示为绝对值，例如 ±0.05 cm³，也可以表示为测量值的百分比。
2. Systematic vs Random Errors | 系统误差与随机误差
Random errors cause readings to scatter around the true value. Repeating a measurement and taking a mean reduces the effect of random errors but does not remove them completely.
随机误差使读数在真实值附近波动。重复测量并取平均值可以减小随机误差的影响，但不能完全消除它们。
Systematic errors cause all readings to be shifted in the same direction. Examples include a balance that has not been zeroed, a thermometer calibrated incorrectly, or a titre value affected by a burette that leaks slowly.
系统误差使所有读数朝同一方向偏移。例如未调零的天平、校准不准确的温度计，或缓慢漏液的滴定管影响滴定体积。
Repeating measurements does not reduce systematic errors. You must identify and correct the source, or use a different instrument or method.
重复测量不能减小系统误差。你必须找出并纠正误差来源，或改用其他仪器或方法。
3. Accuracy and Precision | 准确度与精密度
Accuracy describes how close a measured value is to the true value. A set of results can be precise but inaccurate if they are all affected by the same systematic error.
准确度描述测量值接近真实值的程度。如果一组结果都受到同一系统误差的影响，它们可能精密但不准确。
Precision describes how close repeated measurements are to each other. It is often shown by a small range or small standard deviation.
精密度描述重复测量值彼此之间的接近程度。通常用较小的极差或较小的标准差表示。
In a titration, a student who obtains 24.10, 24.15 and 24.20 cm³ has precise results. If the true titre is 25.00 cm³, the results are precise but not accurate because a systematic error is present.
在滴定中，学生得到 24.10、24.15 和 24.20 cm³，结果是精密的。如果真实滴定体积为 25.00 cm³，则结果精密但不准确，因为存在系统误差。
4. Absolute and Percentage Uncertainty | 绝对不确定度与百分比不确定度
e units as the measurement. A mass of 2.50 ± 0.01 g has an absolute uncertainty of 0.01 g.
绝对不确定度与测量值的单位相同。质量为 2.50 ± 0.01 g 的绝对不确定度为 0.01 g。
Percentage uncertainty allows fair comparison between different sizes of measurement. It is calculated using:
百分比不确定度可以在不同大小的测量值之间进行公平比较。计算公式为：
percentage uncertainty = (absolute uncertainty ÷ measured value) × 100%
For a mass reading of 2.50 ± 0.01 g, the percentage uncertainty is (0.01 ÷ 2.50) × 100% = 0.40%. This is often the value you combine when multiplying or dividing values.
对于质量为 2.50 ± 0.01 g 的读数，百分比不确定度为 (0.01 ÷ 2.50) × 100% = 0.40%。当数值进行乘除运算时，通常需要合成百分比不确定度。
5. Reading and Apparatus Uncertainties | 读数不确定度与仪器不确定度
division. For a burette marked every 0.1 cm³, one reading has an uncertainty of ±0.05 cm³.
对于大多数模拟仪器，读数不确定度是最小刻度分度值的一半。对于每隔 0.1 cm³ 标记的滴定管，单次读数的不确定度为 ±0.05 cm³。
the titre is usually ±0.10 cm³, because two readings are involved: ±0.05 cm³ + ±0.05 cm³.
滴定体积需要两次滴定管读数，即初始读数和最终读数。因此，滴定体积的绝对不确定度通常为 ±0.10 cm³，因为涉及两次读数：±0.05 cm³ + ±0.05 cm³。
The table below shows typical uncertainties used in AQA practical work. Always check the question, because the examiner may state a different value.
下表列出 AQA 实验工作中常用的典型不确定度。答题时务必检查题目，因为考官可能给出不同数值。
| Instrument | Typical absolute uncertainty |
|---|---|
| Burette, single reading | ±0.05 cm³ |
| Burette, titre (two readings) | ±0.10 cm³ |
| Pipette, 25.0 cm³ | ±0.06 cm³ |
| Balance, 2 decimal places | ±0.01 g |
| Thermometer, 1 °C divisions | ±0.5 °C |
| Measuring cylinder, 1 cm³ divisions | 广告 / Sponsored 英国CGP原版 A-Level Chemistry: AQA Year 1 & 2 Complete Revision… 化学 备考教辅 · 正版现货 · 与本文内容相关 查看详情 / View on Taobao参考价 ¥292.0
更多咨询请联系16621398022（同微信） 备考资讯每日更新，关注不错过 考纲变化 · 科目分析 · 学习方法  在微信里长按二维码识别关注 或截图后用「扫一扫 → 相册」选择本图 公众号：tutorhao |