Science Lab · Chemistry

Mixing Lab

A chemistry bench where nothing can spill, burn or fizz over. Test lemon juice, cola and soapy water with four indicators, mix an acid and a base until they cancel, titrate drop by drop and watch the curve jump, then shrink down to the size of molecules and see why heat and a catalyst make a reaction go faster. Every pH is worked out exactly.

Benches

Pour into the beaker

Pour size for water, HCl and NaOH

HCl bottle NaOH bottle

Indicator

Live numbers

Missions

What you're seeing

Acids and bases. The shelf holds eight everyday liquids, pure water, and two lab bottles: hydrochloric acid (HCl), a strong acid, and sodium hydroxide (NaOH), a strong base. Tap a bottle to pour it. The pH meter reads the beaker, the indicator colors it, and every liquid you test gets a marker on the pH scale at the bottom, so the shelf sorts itself into acids and bases as you go.

The everyday liquids show their typical pH from published measurements; real lemons and real coffees vary a little. HCl, NaOH and water can be mixed in any amounts, and then the pH is calculated exactly from what is in the beaker.

Titration. A burette, a long glass tube with a tap, drips NaOH into a flask holding 25.00 mL of acid. The graph draws the titration curve, the pH against the volume of base added, as you go. Tap the tap (or the buttons) to open and close it.

Reaction rates. Here you shrink down to the size of molecules. Blue particles (A) and gold particles (B) fly around a box held at a fixed temperature. When an A hits a B hard enough, they react and turn into pink C and green D. The meter counts reactions per second, the hill shows the energy barrier, and the bar chart sorts every A–B collision by how hard it was.

The science

What pH measures

In water, an acid gives away hydrogen ions, H⁺, which attach to water molecules and form hydronium ions, H₃O⁺. A base does the opposite: it takes them away, which leaves extra hydroxide ions, OH⁻. The pH is a short way to write how much hydronium there is:

pH = −log₁₀[H₃O⁺] [H₃O⁺] in mol/L e.g. [H₃O⁺] = 1.0 × 10⁻³ mol/L → pH 3.00

Even pure water holds a few of both ions, because water molecules trade hydrogen ions with each other. Their concentrations always multiply to the same small number, the ion product of water:

[H₃O⁺] · [OH⁻] = K_w = 1.0 × 10⁻¹⁴ at 25 °C so pH + pOH = 14.00

In pure water both are 1.0 × 10⁻⁷ mol/L, so its pH is 7.00: neutral. Below 7 is acidic, above 7 is basic. Each step of 1 on the scale is a factor of 10, so lemon juice at pH 2.3 has about 50,000 times more hydronium than pure water (10^{7 − 2.3} ≈ 50,000).

Liquid	Typical pH	Source
Lemon juice	2.0 – 2.6	U.S. FDA table of food pH
Cola	about 2.4 (one leading cola measured 2.37)	Reddy et al., 2016
Vinegar	2.4 – 3.4	U.S. FDA table of food pH
Black coffee	about 5	OpenStax Chemistry 2e, Fig. 14.2
Milk	6.4 – 6.8	U.S. FDA table of food pH
Pure water, 25 °C	7.00	OpenStax Chemistry 2e, 14.1
Baking soda in water	about 8.3	worked out from carbonic acid's two acid constants
Soapy water (bar soap)	9 – 10	Tarun et al., 2014
Household ammonia	11 – 12	Penn State; OpenStax Fig. 14.2

Indicators

An indicator is a dye that is itself a weak acid. It has one color with its hydrogen ion on and another with it off, and the pH decides which form wins. Each one changes over its own range:

Universal indicator, a mixture of several dyes: red at pH 3 and below, orange and yellow from 4 to 6, green at 7, blue from 8 to 10, violet from 11. Brands differ a little.
Red cabbage juice, colored by anthocyanins: red near pH 2, purple near 4, violet near 6, blue near 8, blue-green near 10, greenish yellow near 12.
Phenolphthalein: colorless below about pH 8.2, turning pink from 8.2 to 10.
Litmus: red below pH 4.5, blue above 8.3, purple in between.

Neutralization, exactly

Hydronium and hydroxide destroy each other: H₃O⁺ + OH⁻ → 2 H₂O. So when HCl meets NaOH, what counts is moles. The number of moles in a solution is its concentration times its volume, n = c · V, with the concentration in moles per liter (mol/L, which chemists also write M). If the moles of base match the moles of acid, the result is neutral, whatever the volumes: 20 mL of 0.10 mol/L HCl (2.0 millimoles) is neutralized by 10 mL of 0.20 mol/L NaOH (also 2.0 millimoles).

The bench works out the pH from a charge balance: the positive ions (H₃O⁺ and Na⁺) must match the negative ones (OH⁻ and Cl⁻). With D = [Cl⁻] − [Na⁺], the extra acid per liter, that gives one exact answer:

[H₃O⁺] = ( D + √(D² + 4K_w) ) / 2

Far from neutral this is just "the leftover acid," but near pH 7 the water's own ions matter. That is why 1.0 × 10⁻⁸ mol/L HCl has a pH of 6.98, not 8.

Titration

A titration finds out how much acid is in a sample by adding base until the two are used up together. That moment is the equivalence point:

c_acid · V_acid = c_base · V_equivalence 0.100 mol/L × 25.00 mL = 0.100 mol/L × 25.00 mL

Near the equivalence point the curve jumps. In 25.00 mL of 0.100 mol/L HCl, adding NaOH from 24.90 mL to 25.10 mL, about four drops, takes the pH from 3.70 to 10.30. An indicator that changes color inside that jump, like phenolphthalein, marks the end within a drop.

A weak acid such as acetic acid, the acid in vinegar, only gives away a small part of its hydrogen ions. Its strength is measured by its acid constant, K_a = 1.8 × 10⁻⁵, or pK_a = −log K_a = 4.74. While base is added, the flask holds both the acid (HA) and its partner, acetate (A⁻), and the pH follows the Henderson–Hasselbalch equation:

pH = pK_a + log₁₀( [A⁻] / [HA] )

Halfway to the equivalence point, half the acid has become acetate, the two are equal, the log is zero, and pH = pK_a. That is how chemists measure pK_a. Around it lies the buffer region: from about 2 mL to 23 mL of base the pH only climbs from 3.75 to 5.74, because the acid and acetate soak up what is added. Your blood is buffered in a similar way, which keeps its pH near 7.4.

Why reactions go faster

Molecules can only react when they meet, and only if they meet hard enough to break and remake bonds. The smallest energy that works is the activation energy, E_a. Collision theory says the fraction of collisions hard enough is:

fraction = e^{−E_a / RT} R = 8.314 J/(mol·K), T in kelvins RT = 2.48 kJ/mol at 25 °C

That gives the Arrhenius equation for the rate constant, k = A · e^−E_a/RT, where A stands for how often the molecules meet. Three things speed a reaction up:

Concentration. More particles means more meetings. For A + B, doubling A doubles the rate; doubling both makes it four times as fast.
Temperature. Hot particles meet a little more often and, more importantly, far more of them meet hard enough. For a typical barrier of 50 kJ/mol, only about 2 collisions in a billion at 25 °C have the energy. With a barrier of 53 kJ/mol, warming from 25 °C to 35 °C doubles the rate.
A catalyst. It gives the reaction a different path with a lower hill, and it is not used up. The enzymes in your body are catalysts: they let reactions run quickly at 37 °C that would otherwise be far too slow.

Our box uses a small barrier, 7 kJ/mol to start, so that about 6 in every 100 A–B collisions react and you can watch it happen. A small barrier also makes the rate less sensitive to heat: here it takes a rise from 25 °C to about 100 °C to double the rate.

Try this

Ten times weaker, one step up. Rinse the beaker, pour 10 mL of 0.10 mol/L HCl (pH 1.00), then add 90 mL of water. The pH is now 2.00. Every tenfold dilution moves an acid one step toward 7, but no amount of water takes it past 7.

One drop. Pour 10 mL of HCl and 10 mL of NaOH, both 0.10 mol/L: pH 7.00. Now set the pour size to 1 drop (0.05 mL) and add one more drop of NaOH. The pH leaps to 10.40. One drop short would have read 3.60.

Strong and weak. Titrate the HCl, then the acetic acid, at the same concentration. Both need 25.00 mL of base, since both hold the same number of moles of acid. But acetic acid starts at pH 2.87 instead of 1.00, rises slowly through its buffer region, and reaches its equivalence point at pH 8.72, not 7.

The wrong indicator. Titrate acetic acid with litmus, then with phenolphthalein. Litmus drifts from red to blue across the whole buffer region, so you can't tell where to stop. Phenolphthalein stays clear until the jump, then turns pink within a drop.

The mystery acid. Pick Mystery acid, find the equivalence point, and work out its concentration: c_acid = c_base × V_equivalence ÷ 25.00 mL. The panel's Your result line does this sum for wherever you stop, and the true value appears once you've passed the jump.

Barrier and heat. On Reaction rates, heat the box from 25 °C to 100 °C: the rate roughly doubles. Now raise the activation energy to 14 kJ/mol and do it again: the same heating makes it about 3.5 times faster. The higher the hill, the more heat helps.

Running out. Turn off Keep A and B topped up. Now each reaction uses up an A and a B for good, the box fills with C and D, and the rate falls as the reactants run low.

Safety first. Never mix household cleaners. Bleach mixed with ammonia makes toxic gases called chloramines, and bleach mixed with an acid, vinegar included, gives off chlorine gas (Washington State Department of Health). Ammonia and lye-based cleaners also hurt eyes and skin, which is why they stay on the screen here.

At home, with an adult: red cabbage indicator. Chop a few leaves of red cabbage into a bowl and ask an adult to cover them with hot water. Once it has cooled, strain the purple juice into a jar. Pour a little into three clear cups. Stir a spoonful of vinegar into one and a spoonful of baking soda into another, and leave the third as it is. The vinegar cup turns pink-red and the baking soda cup turns blue-green. Then pour some vinegar into the blue-green cup and watch it fizz and change color. Don't drink the results; pour them down the sink and wash the cups when you're done.

A common mix-up

"At the equivalence point, the solution is neutral." Only when a strong acid meets a strong base. Titrate acetic acid and the equivalence point comes at pH 8.72. By then all the acid has turned into acetate ions, and acetate is a weak base: it takes a few hydrogen ions back from water and leaves some OH⁻. "Equivalent" means equal moles of acid and base, not pH 7. It is also why the indicator matters: phenolphthalein, which changes between 8.2 and 10, suits acetic acid, while one that changed at 7 would stop you short.

A related mix-up: "a strong acid is a concentrated acid." Strong means the acid gives away all its hydrogen ions; concentrated means there is a lot of it per liter. A dilute strong acid (0.0010 mol/L HCl, pH 3.00) can be gentler than a concentrated weak one: 5% vinegar, about 0.83 mol/L acetic acid, has a pH near 2.4.

How the simulation works

The pH. Every mixture of HCl, NaOH and water is solved from the charge balance with K_w = 1.0 × 10⁻¹⁴, as shown above. For acetic acid the bench solves [H₃O⁺] + [Na⁺] = [OH⁻] + [A⁻], with [A⁻] = c·K_a / (K_a + [H₃O⁺]), by halving the search interval 80 times. No shortcut formulas are used, so the buffer region, the half-way point and the equivalence point all come out of the same equation.

What's simplified. Everything is at 25 °C. Concentrations stand in for activities, which is excellent for dilute solutions; at 1 mol/L, real solutions read a little differently. The everyday liquids can't be mixed, because each is a mixture of many chemicals; the bench shows their typical pH. Indicator colors follow published charts but are drawn by eye, and a dark liquid like coffee or cola hides them, as it would in real life.

The particles. A and B are hard disks in a flat box with walls held at the chosen temperature. An A–B collision reacts when its energy along the line between the two centers is at least E_a, which is the textbook collision-theory rule; the catalyst halves E_a. The particles are drawn far bigger and slower than real molecules, the box is 2-D, and the reaction gives off no heat. With the supply on, products fade away and a fresh A and B come in for each pair used up, so the amounts stay steady and the rate can be measured.

The rate rule. For disks in 2-D, collision theory predicts N_AN_B/area × 2d × √(πkT/2μ) × e^−E_a/RT reactions per second, where d is the distance between centers at contact and μ the reduced mass, with two small corrections for crowding and for the walls. The panel shows it next to the measured rate.

How it was checked

Test	Result	Expected
Titration table, OpenStax Chemistry 2e 14.7: 0.100 mol/L HCl and acetic acid with 0.100 mol/L NaOH, 19 volumes each	all 38 pH values within 0.006	the book's values, rounded to 0.01
0.100 mol/L acetic acid, no base added	2.875	2.87
Half-way point of the acetic acid titration (12.50 mL)	pH 4.745	p`K`_a = 4.745
1.0 × 10⁻⁸ mol/L HCl, where water's own ions matter	6.978	6.98
Charge balance left over, 10,000 random HCl + NaOH mixtures	2.5 × 10⁻¹⁶ (relative)	0
Collision energies, 145,000 A–B collisions: share with energy ≥ 1, 2, 3, 4, 5 `RT`	0.993, 0.994, 0.994, 0.994, 0.989 × the theory	e⁻¹ … e⁻⁵
A–B collisions per second vs. collision theory, eight setups	0.98 – 1.00 × the theory	1
Share of collisions that react vs. e^−E_a/RT: start, 100 °C, twice the A, catalyst, catalyst at 0 °C, 12 kJ/mol	0.998, 1.013, 1.005, 1.016, 1.019, 0.97	1
Rate at 100 °C ÷ rate at 25 °C	1.99	1.97 (collision theory)
Same, with a 14 kJ/mol barrier	3.7	3.48
Rate with twice as much A	2.16	2.14 (a little more crowding)
Rate with the catalyst; with the catalyst at 0 °C	4.16; 3.52	4.10; 3.45
Average temperature of the particles vs. the walls, eight setups	within 1% (3.5 K at most)	equal
Mirror walls, 300 s, 42,000 A–B bounces: change in kinetic energy	2 × 10⁻¹⁴ (relative)	0

Each rate was measured over 1,200 s of box time (four runs of 300 s), counting from 237 reactions (14 kJ/mol at 25 °C) to 17,648 (catalyst), so the slow cases carry a few percent of counting uncertainty. The 12 kJ/mol row pools twelve runs and 1,651 reactions.

Sources

OpenStax, Chemistry 2e: 14.2 pH and pOH (K_w = 1.0 × 10⁻¹⁴ at 25 °C; pH of coffee and household ammonia, Fig. 14.2) and 14.7 Acid-Base Titrations (titration table, K_a of acetic acid 1.8 × 10⁻⁵, indicator ranges, pH = pK_a at the half-way point).
OpenStax, Chemistry 2e, 12.5 Collision Theory (activation energy and the Arrhenius equation).
U.S. Food and Drug Administration, Center for Food Safety and Applied Nutrition, Approximate pH of Foods and Food Products (2007): lemon juice 2.00–2.60, vinegar 2.40–3.40, cow's milk 6.40–6.80.
A. Reddy, D. F. Norris, S. S. Momeni, B. Waldo and J. D. Ruby, "The pH of beverages in the United States," Journal of the American Dental Association 147, 255 (2016).
J. Tarun et al., "Evaluation of pH of bathing soaps and shampoos for skin and hair care," Indian Journal of Dermatology (2014): most soaps between pH 9 and 10.
Penn State, College of Earth and Mineral Sciences, course notes on pH (ammonia 11 to 12, lemons 2.2 to 3.0).
University of Illinois, Carl R. Woese Institute for Genomic Biology, Cabbage pH indicator activity (color chart).
Wikipedia, Universal indicator (color chart) and Litmus (pH 4.5 to 8.3).
Washington State Department of Health, Dangers of mixing bleach with cleaners.
NIST, CODATA value of the molar gas constant, 8.314462618 J/(mol·K).
D. Henderson, "A simple equation of state for hard discs," Molecular Physics 30, 971 (1975), for the crowding correction.