Hydrates水合物

Big Idea · Scale, Proportion, and Quantity (SPQ)AP Science Practice 5 · Mathematical Routines~35 min

Learning goals

  • Explain what hydrates, water of hydration, and anhydrous compounds are, and read formulas like CuSO₄·5H₂O
  • Name hydrates in English (prefix + hydrate) and recognize their Chinese names
  • Use masses before and after heating to find the number of waters of hydration and the percent water by mass

Before you start

  • Mass ratios and mass percent of elements (1.5.6)
  • Polyatomic ions (2.5.2)

Why do blue crystals turn white when heated?

Heat blue copper(II) sulfate crystals in a test tube, and drops of water collect near the mouth of the tube as the crystals slowly turn into a white powder. Once it cools, add a few drops of water, and the white powder turns blue again. The blue crystals contain water molecules: their formula is CuSO₄·5H₂O. Because white anhydrous copper(II) sulfate turns blue in contact with water, labs use it to test for water.

Hydrates

A crystal that contains a fixed number of water molecules is a hydrate水合物, and that water is its water of hydration结晶水. What remains after all of it is driven off is the anhydrous无水物 compound.

  • The dot in the formula is not a multiplication sign; it means the two parts are combined. 5H₂O means each CuSO₄ unit holds 5 water molecules.
  • A hydrate has a fixed composition: it is a pure substance, not a mixture of salt and water.
  • Losing the water of hydration produces a new substance, so it is a chemical change:
CuSOX4 ⋅ 5 HX2O(s)→ΔCuSOX4(s)+5 HX2O(g)\ce{CuSO4*5H2O(s) ->[\Delta] CuSO4(s) + 5H2O(g)}

Naming hydrates

English name: the name of the ionic compound + a prefix for the number of water molecules (the same prefixes as in lesson 2.5.3) + hydrate. With all the water removed, the compound is anhydrous. Chinese name: number + 水合 + the salt’s name, often with 合 dropped.

FormulaNameChinese nameCommon name
CuSO₄·5H₂Ocopper(II) sulfate pentahydrate五水合硫酸铜blue vitriol (胆矾)
CoCl₂·6H₂Ocobalt(II) chloride hexahydrate六水合氯化钴
MgSO₄·7H₂Omagnesium sulfate heptahydrate七水合硫酸镁Epsom salt
Na₂CO₃·10H₂Osodium carbonate decahydrate十水合碳酸钠washing soda
CaSO₄·2H₂Ocalcium sulfate dihydrate二水合硫酸钙gypsum
CuSO₄anhydrous copper(II) sulfate无水硫酸铜

The number of waters doesn’t have to be a whole number. Heated to about 150 °C, gypsum loses part of its water to become CaSO₄·½H₂O (also written 2CaSO₄·H₂O), calcium sulfate hemihydrate. This is plaster of Paris, which hardens again when mixed with water and is used for casts and molds.

Finding the number of waters

Heat a weighed sample of a hydrate until two weighings in a row give the same mass. This is heating to constant mass恒重, and the mass lost is the water of hydration. Then use the idea from lesson 1.5.6, mass = number × relative mass, so the number of waters per formula unit of salt is

x=mwater÷18.02msalt÷Msaltx = \frac{m_{\text{water}} \div 18.02}{m_{\text{salt}} \div M_{\text{salt}}}

Here M is the formula mass. In lesson 2.6 you will see that this is exactly the mole ratio of the two. These calculations use the atomic masses on the AP periodic table (H 1.008, O 16.00, S 32.06, Cl 35.45, Cu 63.55, Ba 137.33, and so on). Chinese textbooks round most of them to whole numbers (Cu 64, Cl 35.5), so their answers can differ slightly in the last digit.

Choose a hydrate, heat it to constant mass, and find x from the masses in the table:

Try it: heat a hydrate to constant mass and find x, the number of waters of hydration

Example 1: Washing soda

Name Na₂CO₃·10H₂O and find its percent water by mass.

Step-by-step solution

  1. Name. The salt is sodium carbonate, and ten waters take the prefix deca-: sodium carbonate decahydrate.

  2. Formula masses. The water of hydration counts in the crystal’s mass:

    NaX2COX3: 2(22.99)+12.01+3(16.00)=105.9910 HX2O: 10×18.02=180.2total: 105.99+180.2=286.2\begin{aligned} \ce{Na2CO3}: \ & 2(22.99) + 12.01 \\ & + 3(16.00) \\ & = 105.99 \\ \ce{10H2O}: \ & 10 \times 18.02 = 180.2 \\ \text{total}: \ & 105.99 + 180.2 = 286.2 \end{aligned}

  3. Percent water.

    180.2286.2×100%=63.0%\frac{180.2}{286.2} \times 100\% = \boxed{63.0\%}

  4. Check. More than half the mass of washing soda is water, which is why the crystals lose noticeable mass as they dry out. A common mistake is using 18.02 (one water) instead of 10 waters.

Example 2: Finding x from data

A 2.50 g sample of hydrated barium chloride, BaCl₂·xH₂O, is heated to constant mass, leaving 2.13 g of anhydrous BaCl₂. Find x and name the hydrate.

Step-by-step solution

  1. The idea. x is the number of waters per BaCl₂, which is the mole ratio of the two. Start with the mass of water lost.

  2. Mass of water. Heating to constant mass means all the water is gone:

    m(HX2O)=2.50−2.13=0.37 gm(\ce{H2O}) = 2.50 - 2.13 = 0.37\ \text{g}

  3. Moles of each (mol). M(BaCl₂) = 137.33 + 2 × 35.45 = 208.23 g/mol and M(H₂O) = 18.02 g/mol:

    n(HX2O)=0.37/18.02=0.0205n(BaClX2)=2.13/208.23=0.0102\begin{aligned} n(\ce{H2O}) &= 0.37 / 18.02 \\ &= 0.0205 \\ n(\ce{BaCl2}) &= 2.13 / 208.23 \\ &= 0.0102 \end{aligned}

  4. Take the ratio.

    x=0.02050.0102≈2.0⇒x=2\begin{aligned} x &= \frac{0.0205}{0.0102} \approx 2.0 \quad \Rightarrow \quad x \\ &= \boxed{2} \end{aligned}

  5. Name. BaCl₂·2H₂O is barium chloride dihydrate.

  6. A common mistake. Using the mass ratio 0.37 : 2.13 as the count ratio. Numbers of particles follow moles, not grams.

Practice: how many water molecules does each formula unit hold?
  1. copper(II) sulfate pentahydrate
  2. cobalt(II) chloride hexahydrate
  3. magnesium sulfate heptahydrate
  4. sodium carbonate decahydrate
  5. barium chloride dihydrate
  6. lithium hydroxide monohydrate
  7. sodium sulfate decahydrate
  8. nickel(II) chloride hexahydrate
  9. calcium sulfate dihydrate

Common mistakes

Mistake 1: “The dot in CuSO₄·5H₂O means multiply.” The dot means the salt and the water are combined. To find the formula mass, add the two parts: 159.61 + 5 × 18.02 = 249.71, not a product.

Mistake 2: “Blue vitriol is a mixture of copper(II) sulfate and water.” Every CuSO₄ unit in the crystal holds exactly 5 water molecules, so the composition is fixed and it is a pure substance. Losing that water makes a new substance, a chemical change, not simple evaporation.

Mistake 3: “One heating is enough before you weigh.” If some water of hydration remains, the mass loss is too small and so is the value of x. Heat to constant mass: only when two weighings in a row agree is all the water gone.

Quick check

What is the name of Na₂SO₄·10H₂O?

About what percent of the mass of CuSO₄·5H₂O is water?

Summary

  • A crystal holding a fixed number of water molecules is a hydrate; the water is its water of hydration, and with all of it removed the compound is anhydrous. The dot in the formula means “combined with,” and a hydrate is a pure substance.
  • English name: the salt’s name + a prefix + hydrate, as in copper(II) sulfate pentahydrate. Chinese name: number + 水合 + the salt’s name, as in 五水合硫酸铜.
  • Heat to constant mass; the mass lost is water, and water : salt = (mass of water ÷ 18.02) : (mass of salt ÷ formula mass of salt).
On to AP (for later)

Determining the formula of a hydrate is a classic AP lab. The AP version works in moles (lesson 2.6) and also asks how errors would change the result, such as not heating to constant mass, losing sample by spattering, or weighing the crucible while it is still hot.

Practice this chapter: 2.5 · Nomenclature (Focus on English Names) · 10 questions

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