Conductivity of Solutions (Senior 5 Chemistry): free lessons | Ganzaa

Conductivity of Solutions

Lessons

Senior 5 · Chemistry

Conductivity of Solutions

4 lessons

Lesson 1 of 4

Conductance, Conductivity and Electrolytic Conduction

25 min

A number that counts ions

Dip a conductivity probe into water from a laboratory still and the meter reads almost zero. Dip it into tap water and the reading jumps; into sea water and it jumps again, by about a thousand times. Nothing has been added that changes the water molecules themselves. The meter is responding to dissolved ions, because in a solution it is ions, not electrons, that carry the current. Water-treatment plants, breweries, power stations and fish farms all use this one measurement to check how much dissolved salt their water contains.

A conductivity probe standing in a measuring cylinder of freshly distilled water, connected to a hand-held meter. The very low reading shows that the water contains almost no ions. Photo: Encik Tekateki, CC BY-SA 4.0, via Wikimedia Commons

Definition

Resistance, $R$ (unit ohm, Ω) and conductance, $G$ $= \frac{1}{R}$ (unit siemens, S $= \Omega^{-1}$ ).

Conductivity (specific conductance), $\kappa$ (kappa): the conductance of a sample of unit length and unit cross-sectional area; $\kappa = G\frac{l}{A}$ . Units S m⁻¹, or in chemistry usually S cm⁻¹. Example: 0.0100 mol dm⁻³ KCl at 25 °C, $\kappa = 1.413 \times 10^{-3}\,\mathrm{S\,cm^{-1}}$ .

Cell constant, $K_{\text{cell}}$ $= \frac{l}{A}$ (unit cm⁻¹) for a conductivity cell whose electrodes have area $A$ and are a distance $l$ apart, so that $\kappa = K_{\text{cell}} \times G = \frac{K_{\text{cell}}}{R}$ .

Electrolyte: a substance that conducts when molten or in solution because it contains mobile ions.

How a solution conducts

Figure 12.1: A conductivity cell, shown at one instant. Ions drift towards the oppositely charged plate and together carry the current; with AC the polarity reverses about a thousand times a second.

The conductance of the cell depends on the cell's shape as well as on the solution: longer $l$ means more resistance, larger $A$ means less. Conductivity removes the effect of shape, so it describes the solution alone. In practice the cell constant is found by measuring the resistance of a standard KCl solution of known $\kappa$ , rather than by measuring $l$ and $A$ .

Two precautions make the measurement reliable:

Alternating current (about 1 kHz) is used. Direct current would electrolyse the solution, change its composition and coat the electrodes with gas bubbles.
Constant temperature: the conductivity of most electrolyte solutions rises by about 2 % per degree Celsius, because the solvent becomes less viscous and ions move faster.

What makes a solution conduct well?

The concentration of ions: more ions, more carriers.
The charge on the ions: $\mathrm{Mg^{2+}}$ carries twice the charge of $\mathrm{Na^{+}}$ .
The speed (mobility) of the ions: small, heavily hydrated ions such as $\mathrm{Li^{+}}$ drag a large shell of water and move slowly. $\mathrm{H^{+}}$ and $\mathrm{OH^{-}}$ are exceptionally fast because a proton can hop from one water molecule to the next along hydrogen bonds instead of the whole ion moving.
The temperature and the viscosity of the solvent.

Metallic and electrolytic conduction

Property	Metallic conduction (copper)	Electrolytic conduction (NaCl(aq))
Charge carriers	delocalised electrons	positive and negative ions
Chemical change?	none	yes, at the electrodes (electrolysis, with DC)
Matter transported?	no	yes, ions move through the liquid
Effect of raising temperature	conductivity falls (more lattice vibration scatters electrons)	conductivity rises (ions move faster)
Typical conductivity / S cm⁻¹	$6.0 \times 10^{5}$	about $10^{-3}$ to $10^{-1}$

Worked example

Problem. A conductivity cell filled with 0.0100 mol dm⁻³ KCl ( $\kappa = 1.413 \times 10^{-3}\,\mathrm{S\,cm^{-1}}$ at 25 °C) has a resistance of 707 Ω. Filled with a sample of river water at 25 °C, its resistance is 1250 Ω. Calculate (a) the cell constant; (b) the conductivity of the river water.

Solution. (a) $K_{\text{cell}} = \kappa R = 1.413 \times 10^{-3} \times 707 = 0.999\,\mathrm{cm^{-1}}$ .

(b) $\kappa = \frac{K_{\text{cell}}}{R} = \frac{0.999}{1250} = 7.99 \times 10^{-4}\,\mathrm{S\,cm^{-1}} = 799\,\mu\mathrm{S\,cm^{-1}}$

Answer: (a) 0.999 cm⁻¹; (b) $7.99 \times 10^{-4}$ S cm⁻¹. The same cell, same temperature: only the solution changed.

Worked example

Problem. The plates of a cell each have area 1.50 cm² and are 0.600 cm apart. With a solution in the cell, the conductance is $2.40 \times 10^{-3}$ S. Calculate the cell constant and the conductivity, and state the conductivity in S m⁻¹.

Solution. $K_{\text{cell}} = \frac{l}{A} = \frac{0.600}{1.50} = 0.400\,\mathrm{cm^{-1}} \qquad \kappa = G K_{\text{cell}} = 2.40 \times 10^{-3} \times 0.400 = 9.60 \times 10^{-4}\,\mathrm{S\,cm^{-1}}$

1 S cm⁻¹ = 100 S m⁻¹ (there are 100 cm in 1 m, and cm is in the denominator), so $\kappa = 9.60 \times 10^{-2}\,\mathrm{S\,m^{-1}}$ .

Warning

Unit traps. S cm⁻¹ to S m⁻¹: multiply by 100, not divide. µS cm⁻¹ (microsiemens per centimetre) is the unit on most water meters: $1\,\mu\mathrm{S\,cm^{-1}} = 10^{-6}\,\mathrm{S\,cm^{-1}}$ . Always quote the temperature with a conductivity.

Safety: conductivity meters use low voltages and are safe, but never test a solution's conductivity with a mains-powered lamp circuit. Wash the probe with distilled water between samples, and handle salt and acid solutions with goggles.

Tip

Think of $\kappa$ as "conductance of a 1 cm cube of solution". A cell with $K_{\text{cell}} = 1.00\,\mathrm{cm^{-1}}$ behaves like that cube, so its conductance in siemens equals the conductivity in S cm⁻¹.

Ekeeda: Cell Constant and Its Determination. Watch how the cell constant links the measured resistance to the conductivity, and how a standard KCl solution is used to find it.

✦

Practice

Define conductivity and give its SI unit.
A cell has $K_{\text{cell}} = 1.20\,\mathrm{cm^{-1}}$ . With a solution, $R = 400\,\Omega$ . Calculate $\kappa$ in S cm⁻¹ and in S m⁻¹.
Why is alternating current, not direct current, used to measure the conductivity of a solution?
The conductivity of a solution is $1.29 \times 10^{-2}\,\mathrm{S\,cm^{-1}}$ and the cell's resistance is 85.0 Ω. Calculate the cell constant.
Explain why the conductivity of copper falls slightly as it is heated, while the conductivity of NaCl(aq) rises.
Explain why 0.01 mol dm⁻³ HCl conducts far better than 0.01 mol dm⁻³ NaCl, although both are fully ionised.
A student reports that tap water has "a conductivity of 450". Evaluate this report.

Show answersHide answers

The conductance of a sample of unit length and unit cross-sectional area, $\kappa = G\frac{l}{A}$ ; unit S m⁻¹.
$\kappa = \frac{1.20}{400} = 3.00 \times 10^{-3}\,\mathrm{S\,cm^{-1}} = 0.300\,\mathrm{S\,m^{-1}}$ .
DC would cause electrolysis: products would form at the electrodes, the composition would change and gas bubbles would block the electrodes, all changing the resistance.
$K_{\text{cell}} = \kappa R = 1.29 \times 10^{-2} \times 85.0 = 1.10\,\mathrm{cm^{-1}}$ .
In copper, heating increases lattice vibrations, which scatter the moving electrons. In the solution, heating lowers the viscosity of water and the ions move faster, while the number of carriers is unchanged.
The $\mathrm{H^{+}}$ ion has a much higher mobility than $\mathrm{Na^{+}}$ (limiting molar conductivities 349.7 and 50.1 S cm² mol⁻¹), because protons hop along hydrogen-bonded water molecules.
Incomplete: a conductivity needs a unit (450 µS cm⁻¹ is typical of tap water; 450 S cm⁻¹ is impossible) and a temperature, because conductivity changes by about 2 % per °C.

Sources and credits

Conductivity of standard KCl and of copper, and limiting ionic conductivities: CRC Handbook of Chemistry and Physics.
Image: Conductivity Meter using Hanna HI8033.jpg by Encik Tekateki, via Wikimedia Commons, licensed under CC BY-SA 4.0.
Video: Cell Constant and Its Determination, Ekeeda, embedded from YouTube.
The text, Figure 12.1, the table, worked examples and Practice items were written and drawn by Ganzaa.
This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1A number that counts ions

2How a solution conducts

3What makes a solution conduct well?

4Metallic and electrolytic conduction

A number that counts ions

How a solution conducts

What makes a solution conduct well?

Metallic and electrolytic conduction