GCSE化学滴定 终点判断 浓度计算 误差分析
滴定是 GCSE 化学里少数把动手操作和计算连在一起的实验。做错一步,后面所有数字都会跟着错:滴定管上少读或多读 0.1 cm3,反算出来的浓度就差 0.4% 左右。这篇按考纲要求把装置、计算、误差方向三块拆开,配两道用考试局手册数据算的例题。
A titration is one of the few GCSE chemistry experiments where bench technique and arithmetic are graded together, so a single slip carries through every later number. On a burette, 0.1 cm3 is worth roughly 0.4% of a concentration, which is the difference between a clean answer and a marked-down one. What follows separates the apparatus, the calculation and the direction of errors, using figures taken from the exam boards' own practical guidance.
滴定在测什么:用体积比换摩尔比
滴定要回答的问题很具体。把一份体积已知、浓度未知的溶液用移液管放进锥形瓶,再从滴定管滴入浓度已知的另一份溶液,直到两者恰好反应完,读掉下去的体积。未知那一份的浓度,靠这条体积记录和配平方程里的摩尔比反算。AQA 的 GCSE 化学考纲 8462 把要求放在 4.4.2.5,Required practical 2 的措辞是测定强酸与强碱溶液的反应体积,并且只在单独化学里要求。强酸和强碱之间反应彻底,终点颜色变化干脆,计算不必考虑水解平衡。换成弱酸或弱碱就麻烦得多,等当点的 pH 不再停在 7,指示剂的选择要跟着变,这也是考纲只把强酸强碱滴定列进必做实验的原因。
A titration answers one narrow question: how much of a solution of known concentration must be delivered from a burette before the amount already sitting in the conical flask has reacted exactly. The unknown concentration is then back-calculated from that delivered volume together with the mole ratio in the balanced equation, which is why AQA places the requirement at 4.4.2.5 and words Required practical 2 as determining the reacting volumes of a strong acid and a strong alkali by titration. Restricting the work to strong solutions keeps the reaction complete and the colour change abrupt, so the arithmetic rests on volume measurement rather than on equilibrium behaviour.
装置与读数:滴定管读到 0.05 cm3
25.0 cm3 的移液管把待测液送进 250 cm3 锥形瓶,滴定管夹在铁架台上,瓶下垫一块白瓷板。移液管要配洗耳球,不能直接用嘴吸。滴定管细长,刻度从上往下增大,读数时平视凹液面最低点,记到 0.05 cm3,也就是小数点后两位、末位是 0 或 5。眼睛跟液面不同高的时候,俯视会把读数读小,仰视会读大,单次差 0.1 cm3 就足以改掉结果的第二位有效数字。装完液先放掉一点,让尖嘴充满并赶走气泡。这一步最容易漏,漏了以后每次读数都把气泡的体积算了进去。白瓷板不是为了好看,深色背景下浅粉色根本看不出来。
A 25.0 cm3 volumetric pipette delivers the solution into a 250 cm3 conical flask, with the burette clamped above it and a white tile underneath; the tile exists so that a faint pink is visible at all. Burette graduations increase downwards, so readings are taken at eye level from the bottom of the meniscus and recorded to the nearest 0.05 cm3, meaning two decimal places ending in 0 or 5. Running a little liquid through the jet after filling expels the air bubble, and the funnel has to come out before any reading, because a drop hanging in it would falsify the start volume.
操作顺序:粗滴定位,精确滴收尾
先做一次粗滴。滴定管记录初读,然后以 1 到 3 cm3 一份的速度往下放,边放边旋摇锥形瓶,看到颜色变掉就立刻关阀,记下终读。粗滴唯一的作用是告诉你终点大概落在哪个体积,它的数值本身不进平均值。第二次开始就按粗滴结果操作:快到终点时先一次加到差 2 到 3 cm3 的位置,然后半滴半滴地放,最后把挂在尖嘴上的半滴用洗瓶水冲下去。旋摇要一直做,不摇的话瓶底局部过量,颜色会提前变,你就把终点读早了。放液速度也要压住,前段可以快,临近终点必须一滴一滴,一滴大约 0.05 cm3,连续放流很容易冲过终点,只能整瓶重来。
The first run is a rough titration: record the start volume, run liquid in at 1 to 3 cm3 a time while swirling, and close the tap the moment the colour goes. Its only job is to show roughly where the end point lies, and its value never enters the mean. From the second run onwards, add quickly to within 2 or 3 cm3 of the rough figure, then proceed drop by drop, washing the last half-drop from the jet into the flask. Swirling continues throughout, since a still flask lets the bottom go locally alkaline and the colour turns early, which reads as a short titre.
终点与指示剂:酚酞和甲基橙的分工
酚酞在酸里无色,在碱里粉红,所以瓶里装碱、滴定管装酸时,终点是粉色刚好褪掉。甲基橙在酸里红、在碱里黄,适合反过来装的场合。Edexcel 的 CP5 教师手册明确说两种指示剂都可以用,学生要同时知道这两种颜色变化。万能指示剂不能用,它一路从红过渡到紫再到蓝绿,没有一个干脆的突变点,读数只能靠猜。判断终点靠的是颜色稳定三十秒不回来,不是颜色变一半就算。
Phenolphthalein is colourless in acid and pink in alkali, so with alkali in the flask and acid in the burette the end point is the moment the pink disappears. Methyl orange runs red in acid and yellow in alkali and suits the reverse arrangement, and the Edexcel CP5 teachers' sheet states that either indicator is acceptable as long as both colour changes are known. Universal indicator is useless here because it slides from red through purple to blue-green with no sharp jump, leaving the reading to guesswork. A genuine end point holds its colour for about thirty seconds rather than half-changing and drifting back.
摩尔计算:从 cm3 到 mol/dm3
拿 AQA 实验手册里的数字走一遍。25.0 cm3、0.100 mol/dm3 的氢氧化钠,用硫酸滴,平均用掉 15.60 cm3。先算碱的物质的量,n = c 乘 V = 0.100 乘 0.0250 = 0.00250 mol。方程 H2SO4 + 2NaOH -> Na2SO4 + 2H2O 里酸和碱是 1 比 2,所以硫酸是 0.00125 mol。再用它除以自身体积 0.01560 dm3,得到 0.0801 mol/dm3,和手册给出的 0.08 mol/dm3 对得上。体积必须先换成 dm3,直接拿 cm3 去除会差一千倍。
Take the figures printed in AQA's practical handbook: 25.0 cm3 of 0.100 mol/dm3 sodium hydroxide titrated with sulfuric acid, mean titre 15.60 cm3. The amount of alkali is n = c x V = 0.100 x 0.0250 = 0.00250 mol. In H2SO4 + 2NaOH -> Na2SO4 + 2H2O the acid to alkali ratio is 1 to 2, so the acid amounts to 0.00125 mol. Dividing by its own volume of 0.01560 dm3 gives 0.0801 mol/dm3, matching the 0.08 mol/dm3 quoted by AQA. Converting cm3 into dm3 first is not optional, since skipping it shifts the answer by a factor of a thousand.
质量浓度换算:乘以摩尔质量
mol/dm3 换成 g/dm3 只差一个摩尔质量。硫酸的 Mr 是 98.1,0.0801 乘上去得 7.86 g/dm3。换一道 1 比 1 的题:25.0 cm3 未知浓度的氢氧化钠,用 0.100 mol/dm3 盐酸滴,平均 23.05 cm3,则盐酸是 0.002305 mol,氢氧化钠同量,浓度 0.002305 除以 0.0250 得 0.0922 mol/dm3。再乘氢氧化钠的 Mr 40.0,得到 3.69 g/dm3。AQA 的 Higher Tier 要求两种单位都会算,题目常常先问 mol/dm3 再追一句 g/dm3。已知 g/dm3 反求 mol/dm3 时先除摩尔质量,不要两步并成一步心算。
Converting mol/dm3 into g/dm3 needs nothing but the molar mass: sulfuric acid at Mr 98.1 gives 0.0801 x 98.1 = 7.86 g/dm3. A 1 to 1 case runs the same way, with 25.0 cm3 of sodium hydroxide of unknown concentration requiring a mean 23.05 cm3 of 0.100 mol/dm3 hydrochloric acid; that is 0.002305 mol of acid, hence the same amount of alkali, and 0.002305 divided by 0.0250 gives 0.0922 mol/dm3. Multiplying by Mr 40.0 turns it into 3.69 g/dm3. Higher Tier candidates at AQA are expected to produce both units, and papers routinely ask for mol/dm3 first and g/dm3 as a follow-up, so divide by the molar mass cleanly instead of folding both steps into mental arithmetic.
一致性判断:哪几个读数能取平均
平行滴定的结果要挑"一致"的那几个取平均。所谓一致,就是两次滴定体积相差很小,通常在一次滴定的读数精度量级上。Edexcel 的 CP5 教师手册写的是相差 0.2 cm3 以内即可取平均,不同考试局给的阈值不完全一样,做题时以本局给的表为准。粗滴哪怕数值看着很漂亮也不进平均,它加得太快,误差结构和其他几次不同。表格里通常留三到四行,一行粗滴加两三行平行,平均值只对后几行算,把被丢掉的那行划掉比留着更清楚。手册还点出考生错得最多的就是这一点:把包括粗滴在内的所有结果一起平均。
Repeats are averaged only where they agree, which in practice means their titres differ by no more than the precision of a single reading. The Edexcel CP5 teachers' sheet allows 0.2 cm3 and other boards set their own threshold, so follow the table printed in the paper you are sitting. The rough run stays out of the mean even when its number looks neat, because it was added too fast and its error profile differs from the rest. That is precisely the mistake Pearson flags as the most common one in examinations: averaging every result, rough run included.
误差来源:洗涤、气泡、漏斗与读法
洗涤规则按容器分开记。滴定管要用待装的酸润洗两三次,管壁残留的水会把酸稀释。移液管要用待移的溶液润洗,残留水会稀释瓶里的碱。锥形瓶只用蒸馏水洗,瓶里那点水不改变溶质的物质的量,因为体积是由移液管定量给的。气泡留在尖嘴,放出去的液体先去填气泡,读数就比真实用量大。漏斗没取下来,一滴残液落进管里,初读也是假的。加指示剂几滴就够,倒多了终点会拖后。
Rinsing follows the container. A burette is rinsed with the acid it will hold, because water left on the walls dilutes it; a pipette is rinsed with the solution it will deliver, for the same reason in the other direction. The conical flask is rinsed with distilled water only, since the residual water cannot change the amount of solute when the volume itself is fixed by the pipette. An air bubble trapped in the jet is spent first, so the recorded volume exceeds what actually reached the flask, and a funnel left in place drops liquid in and corrupts the start reading. A few drops of indicator suffice, as an excess drags the colour change past the true end point.
误差方向:结果偏高还是偏低
写误差题要落到方向上,不能只写"有误差"。滴定管没润洗,酸被稀释,要中和同样多的碱就得放更多体积,于是用 V 乘 c 算出的碱浓度偏高。移液管只用水润洗,瓶里的碱被稀释,所需酸的体积偏小,算出的碱浓度偏低。尖嘴里的气泡被算成酸的体积,读数偏大,结果偏高。读数时俯视或仰视会让初读和终读同时偏移,若两次视角一致,差值往往相互抵消,只影响单次读数的记录格式。用错指示剂则是另一类问题,它把终点搬到 pH 跳变之外的位置,体积本身读得再准也偏,方向取决于指示剂变色区间落在真实等当点的哪一侧。0.10 cm3 的偏差落在 23.05 cm3 上,相对误差是 0.43%,写答案时按这个量级说影响。
Error questions earn marks for direction, not for the word "error". A burette that was never rinsed holds diluted acid, more volume is needed to neutralise the same amount of alkali, and the concentration calculated from V x c comes out too high. A pipette rinsed with water only dilutes the alkali in the flask, the titre falls short, and the answer comes out too low. An air bubble counted as acid inflates the volume and therefore the result, whereas reading the meniscus from above or below shifts both the start and the end reading; matching viewpoints largely cancel in the difference. A 0.10 cm3 deviation against 23.05 cm3 is 0.43% relative error, which is the scale to quote.
有效数字与记录格式
记录滴定体积的格式是硬性的:每次初读和终读都写到小数点后两位,末位只能是 0 或 5,比如 0.15、23.05。表格里 titre 一栏是终读减初读,不是直接把读数抄过去。中间结果不要提前四舍五入,先把摩尔数算到四位有效数字,最后一步再按题目要求的位数收。有效数字给少了显得仪器精度被浪费,给多了等于声称滴定管能读到 0.001 cm3。写百分误差时用偏差除以平均值再乘一百,单位一致再动手。
Recording format is rigid: every start and end reading carries two decimal places and ends in 0 or 5, as in 0.15 or 23.05, and the titre column is the end reading minus the start reading rather than a copied number. Intermediate values stay unrounded, with amounts carried to four significant figures and the final answer trimmed to whatever the question asks for. Too few figures wastes the precision of the apparatus, too many claims a burette readable to 0.001 cm3. Percentage error is the deviation divided by the mean, multiplied by a hundred, once the units match.
考纲差异:AQA 化学、组合科学与 Edexcel CP5
AQA 8462 的 Required practical 2 覆盖 AT 1 与 AT 8,并且只有单独的化学考,组合科学 Trilogy 和 Synergy 都不做这个实操,AQA 在实验手册里写明实操 2 和 7 属化学独有。用 mol/dm3 与 g/dm3 反算浓度是 Higher Tier 才要求的部分。Edexcel 把它编成核心实验 CP5,对应 C5.9C 和 C5.10C,后者标注 H,甲基橙与酚酞都可选。WJEC 与 OCR 各有自己的实操清单与编号,同一个实验在不同考纲里的叫法和评分点不完全一样,备考时对着本局考纲的 practical 列表逐条核对。考纲多年沿用同一套表述,但版本号会更新,AQA 8462 的考纲从 2016 年首次教学起用到现在的 1.2 版(2026 年 1 月),条目编号没变,引用时写清版本更稳妥。
Required practical 2 in AQA 8462 covers AT 1 and AT 8 and exists only in the separate chemistry qualification, with the handbook stating that practicals 2 and 7 are chemistry only and absent from both Trilogy and Synergy. Turning a titre into mol/dm3 and then g/dm3 belongs to Higher Tier. Edexcel numbers the same work as core practical CP5, tied to C5.9C and the higher-tier C5.10C, and accepts methyl orange or phenolphthalein. WJEC and OCR each publish their own practical list with their own numbering, so the naming and the mark scheme differ from board to board and revision should follow the list printed by the board you sit with.
六分题怎么写:仪器、步骤、终点、平均
描述题按步骤给分,写的时候按仪器、体积、终点、平均四段走。仪器段写 25.0 cm3 移液管配洗耳球移取碱液入锥形瓶,滴定管装酸并赶走气泡。步骤段写先粗滴定位,再逐滴接近终点,全程旋摇。终点段写白瓷板上看颜色由粉转无色并保持,读初读与终读到 0.05 cm3。平均段写重复到两次结果接近,粗滴不计入。很多学生以为写上"摇匀"就算写了操作,评分点其实落在体积准确与终点判断上。模板背下来以后,换酸碱组合只要改指示剂颜色。
Descriptive answers are marked step by step, so build them in four blocks: apparatus, procedure, end point, average. Name the 25.0 cm3 pipette with its filler for the alkali and a burette for the acid with the bubble expelled. State the rough run to locate the end point, then dropwise addition with continuous swirling as it approaches. Place the flask on a white tile and record the colour change from pink to colourless that persists, taking start and end readings to 0.05 cm3. Finish with repeats that agree and an explicit note that the rough titre is excluded, because candidates often write "shake well" and lose the marks that sit on accurate volume and end-point judgement.
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