让我们观察一杯在桌上放置了一天的牛奶会发生什么情况？

It has curdled and turned sour. Put a few drops of a universal indicator solution into the bowl of fresh milk as well as the curdled one. We see that the red colour produced in the curdled milk is brighter. This shows that the curdled milk is more acidic than the fresh one. But how much more acidic is the curdled milk than the fresh one?

牛奶会凝结变酸。将少量通用指示剂分别同时滴入新鲜的牛奶和凝结的牛奶中。我们将看到在凝结的牛奶中，红色更深。这表明凝结牛奶酸性强于新鲜的牛奶。那么凝结牛奶的酸性较新鲜牛奶的酸性强多少呢？

The answer to this question can be found out by reacting known volumes of both the samples with a suitable base, in the presence of an indicator. This process is called an acid base titration.

通过将已知体积的两种样品与适当的碱进行反应，并使用恰当的指示剂，就可以找到这个问题的答案。该过程被称为酸碱滴定。

To understand the principle behind titration, let's consider a reaction between hydrochloric acid and a 1 molar sodium hydroxide solution. Here, the sodium hydroxide solution, whose concentration is known, is called a standard solution. Take 10 ml of this standard solution in an Erlenmeyer flask. A burette, which is a long graduated tube with a capacity of 100 ml and a stopper at the bottom is filled with the HCl solution. Before starting the procedure, two to three drops of an indicator, such as phenolphthalein, are added to the solution in the flask. Phenolphthalein turns pink in a basic solution like that of NaOH, hence the colour of the solution in the conical flask turns pink.

为了理解酸碱滴定的原理，让我们考虑一下盐酸和1mol氢氧化钠溶液之间的反应。这里，浓度已知的氢氧化钠溶液被称为标准溶液。取10ml标准溶液置于锥形瓶中。在滴定管中装入HCl溶液（滴定管是底部装有塞子、容积为100ml的长刻度管）。在开始操作之前，在锥形瓶的溶液中滴入2至3滴指示剂，如酚酞。酚酞会在诸如NaOH之类的碱性溶液中变为粉色，因此锥形瓶中的溶液颜色会变为粉色。

As soon as we start adding HCL from the burette, into the NaOH solution, the chemical reaction starts. During this reaction, the acid and the base molecules react to form a salt such as sodium chloride along with water. This reaction is called neutralization. The conical flask is agitated continuously to ensure a proper mixing of the two solutions. As acid gets added to the NaOH solution, more and more salt and water are formed. The concentration of the NaOH goes on decreasing due to its neutralization by HCl. When all the NaOH reacts with the HCl, we get a neutral solution in the Erlenmeyer flask, and the solution thus turns colourless. This is called the equivalence point or the end point of the reaction. At this stage, the number of equivalents of HCl and NaOH which have reacted with each other is equal.

一旦我们开始从滴定管中向装有NaOH溶液的锥形瓶中加入HCL，化学反应便开始。反应过程中，酸分子和碱分子反应生成盐（即氯化钠）和水。该反应被称为中和反应。在滴入盐酸的过程中不断搅拌锥形瓶中的溶液，确保两种溶液能够有效混合。当将酸加入到碱溶液中时，越来越多的盐和水开始生成。由于与HCL发生了中和反应，NaOH的浓度不断下降。当所有NaOH与HCL反应完全时，锥形瓶中的溶液变为中性溶液，因此溶液变为无色。我们将此时称为等当点或反应的滴定终点。在这个阶段，参与反应的NaOH与HCL是等量的。

The reading on the burette is used to calculate the number of equivalents of HCl. We can see that, 20 ml of hydrochloric acid solution of an unknown concentration has reacted completely with 10 ml of a 1 molar NaOH solution.

滴定管上的读数用于计算HCL的用量。我们能够看到，20ml的未知浓度的盐酸溶液与10ml 1mol的NaOH溶液完全反应。

It is clear from the chemical equation that 1 mole of NaOH reacts completely with 1 mole of HCl. The number of moles of HCl in a given solution is given by (M multiplied by V), where 'M' is the molarity of HCl in moles per litre and V is the volume of the solution in litres.

从化学方程式中可以轻易得出1mol的HCL与1mol的NaOH完全反应。通过“M乘以V” 得到所给溶液中的HCL的摩尔值，这里“M”代表HCL的摩尔浓度（单位为摩尔每升），“V”代表溶液的体积（单位为升）。

Thus, from the chemical equation, (M times V) of HCl is equal to (M times V) of NaOH. This equation is often referred to as the 'Law of molarities'

因此，从化学方程式可以得知，“M乘以V”的HCl等价于“M乘以V”的NaOH。这种等式通常被称为“摩尔定律”。

Substituting the values of the known parameters in the above equation, we get, M times 20 divided by 1000 is equal to 1 times 10 divided by 1000. Thus, molarity of HCl (M) is equal to 1 times 10 divided by 20, which is equal to 0.5 M.

将已知参数的值代入上述等式，我们可以得到以下等式：M乘以20除以1000等于1乘以10除以1000，因此，HCl的摩尔浓度（M）等于1乘以10除以20，即0.5M。

If instead of HCl, a sample of sulphuric acid is titrated against sodium hydroxide, the chemical reaction taking place in the flask will be different. Here, sodium hydroxide gets neutralized by sulphuric acid and sodium sulphate is formed, along with water. One mole of sulphuric acid reacts with 2 moles of sodium hydroxide to form 1 mole of sodium sulphate and 2 moles of water. Thus, the ratio of the number of moles of H₂SO₄ and NaOH, which react completely with each other is 1 is to 2.

如果使用氢氧化钠溶液测定的不是HCl的浓度，而是硫酸的浓度，锥形瓶中的化学反应将完全不同。这里，氢氧化钠溶液与硫酸溶液反应生成硫酸钠和水。1mol硫酸与2mol氢氧化钠反应生成1mol硫酸钠和2mol水。因此，如果反应完全，H₂SO₄ 和NaOH的摩尔比应该为1比2。

In other words, (M times V) of H₂SO₄ is equal to 2 times the product of M and V of NaOH. Therefore, Molarity of H₂SO₄ is equal to 2 times the product of the molarity of NaOH and the volume of NaOH, upon the volume of H₂SO₄.

也就是说，H₂SO₄ 的“M乘以V”等于NaOH 的“M乘以V”的2倍。因此，H₂SO₄的摩尔浓度等于NaOH的摩尔浓度与NaOH体积乘积的2倍除以H₂SO₄的体积。

Hence, the concentration of an acid or a base can be found out using the titration method.

因此，酸或碱的浓度能够使用滴定法进行测定。

Note here that, as the calculations of the concentrations of the solution involve the volumes of the reacting solutions, this process is often called as the volumetric analysis.

在此值得注意的是，因为溶液浓度的计算涉及到反应溶液的体积，因此这种方法同样被称作容量分析。