# A study of the rate of a candle burning

## Introduction

In this investigation, students will study the rate of burning of a candle as a function of the mass of the candle and as a function of the concentration, or partial pressure of O2(g).

Candle wax is a hydrocarbon (ca C25H52). It combusts according to:

wax(s)  +  O2(g)  → CO2(g)  +  HOH(g)     (Equation 1)

(Wax burns as a vapour, but we indicate it as a solid; the mass of the solid is measured here.)

The rate law equation for this reaction is:

rate  =  k(solid wax)x[O2]y    (Equation 2)

In our lab we will burn the candle in air, in which [O2] is constant. Therefore, equation 2 becomes

rate  =  kobserved(solid wax)x,
where  kobserved = k[O2]y = constant    (Equation 3)

Typical values for x are 0, 1 or 2, but higher integer values and even fractions are possible.

If x = 0, the reaction is zero-order with respect to the wax;
If x = 1, the reaction is first-order with respect to the wax;
If x = 2, the reaction is second-order with respect to the wax… you get the idea.

Later in this investigation students examine data for the combustion of a candle at increasing elevations above sea level, where the concentration (or partial pressure) of O2(g) is lower. This will allow students to determine the value of the exponent “y”.

## Purpose

To determine the rate of the reaction and the reaction order of wax(s) and of O2(g) using the equation
rate  =  k[wax]x[O2]y.

## Materials

• small candle, such as a tea light
• small beaker
• matches
• electronic balance
• timing device

## Safety precautions

Wear safety glasses; tie back hair and loose clothing. Make sure matches are extinguished before putting them in the garbage — not the sink.

## Pre-lab questions or class discussion

1. a) How do you expect that the rate of burning will vary with the mass (or length) of the candle?

b) Based on your prediction in part (a) sketch the following graphs:mass of wax (y-axis) versus time (x-axis); burning rate (mass of wax per second) versus time.

## Procedure

### Part 1.  Determination of “x”

1. Read the procedure and analysis questions before you begin. Use prepare a data table in which you record your findings and put calculated data. Place a heading at the top of each column.
2. Place the tea light on an inverted small beaker. Ignite the candle, letting it burn for about two minutes in order to melt the wax near the wick.
3. Start your timer and immediately record the mass of the candle. Record the mass of the candle every 60 s for at least five minutes.

## Analysis

### Determination of “x”  (Order of reaction with respect to solid wax)

1. a) Plot a graph of mass of candle versus time. Use spreadsheet  software to determine the equation of the line of best fit and the corresponding R2 value.
2. b) Plot a graph of [∆mass•time–1 in g•s–1] of the candle on the
y-axis, versus time on the x-axis.
3. a) Comment on the shape of your graphs. That is, are they linear/horizontal/vertical/parabolic/etc?
4. What is the order of the reaction (the value of “x”) with respect to  solid wax?

## Sample results  ### Part 2.  Determination of “y” (Order of reaction with respect to [O2])

4.  To determine how the partial pressure, which is related to
concentration of O2(g) in the air, affects the rate of combustion of a candle, use the data below to plot a graph of combustion rate (g•min–1) versus PPO2 — use spreadsheet software. The data were obtained by Crescent School students on the slopes of Mount Kilimanjaro (outreach trips to Tanzania). They burned candles at increasing elevations above sea level. (Since air is 21% O2 by volume and by pressure, the partial pressure of O2 can be obtained by multiplying the atmospheric pressure (Patm) by 0.21.) 2017 Crescent School trip to Mount Kilimanjaro

The following table has the combustion rate of a candle at increasing elevation above sea level. Partial pressure of O2 can be calculated and filled in.

Elevation
above sea level (m)

Patm
(kPa)

Partial pressure O2
(kPa)
[PPO2 = 21% of Patm]

Rate of wax combustion (g.min-1)
990 90.0 (to be filled in) 1.61 x 10-1
2700 72.4   1.30 x 10-1
3720 63.9   1.09 x 10-1
4700 56.2   9.06 x 10-2

5. What measurements did the students who obtained these data record?

6. Plot a graph of rate of wax combustion (y-axis) versus PPO2. From
your graph determine as quantitatively as possible, the effect of the PPO2 on reaction rate.

7. What is the order of the reaction with respect to PPO2?

## Conclusion

8. Rewrite Equation 2 with suitable values for the exponents. ## Notes

Toronto, Canada is at 76 m, typically around 102 kPa. In this analysis we assumed that the temperature of the burning candle is the same at the different altitudes. If this is not the case, our rate data collected on the mountain slope would reflect both the effect of a (presumably) decreasing flame temperature and the decreasing partial pressure of oxygen.