#8Q1) Mechanics and Properties of Matter

Determination of the relative density of a liquid using Hare’s apparatus

DifficultyMedium
Est. Time45 mins

Required Apparatus

Hare's apparatus, a plastic syringe of about 15 cm, water and a copper sulphate solution or any other suitable solution, a half-metre ruler, and a set square.

Scientific Theory

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  • hwh_{w}: height of water column above water level of beaker
  • hlh_{l}: height of liquid column above liquid level of beaker
  • ρw\rho_{w}: density of water
  • ρl\rho_{l}: density of liquid

If p0p_{0} is the atmospheric pressure and pp the pressure of air in the tube,

p0=p+hwρwg=p+hlρlgp_{0}=p+h_{w}\rho_{w}g=p+h_{l}\rho_{l}g hwρw=hlρlh_{w}\rho_{w}=h_{l}\rho_{l} hw=(ρlρw)hlh_{w}=(\frac{\rho_{l}}{\rho_{w}})h_{l}

Gradient of the graph hwh_{w} against hl=ρlρw=h_{l} = \frac{\rho_{l}}{\rho_{w}} = relative density of liquid.

Experimental Method

  1. Arrange Hare's apparatus as shown in Figure 8.1 with its limbs having ends dipped into water and liquid beakers.
  2. Open the clip and suck air out either by mouth or by the syringe to form a water column and a liquid column in the respective limbs (until the liquid column of lower density reaches maximum height) and then close the clip.
  3. Adjust each index until its tip touches the respective liquid level.
  4. With the help of the set square and using scales measure height hwh_{w} of water column and height hlh_{l} of liquid column and record these readings.
  5. Loosening the clip slightly and again tightening it alternatively obtain a set of values of hwh_{w} and hlh_{l} and record these values.

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Important Points

1
  • State the methodology of using simple measuring instruments to measure accurately the heights of liquid columns.
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  • If a Hare's apparatus with indexes is used for this experiment, the theory as well as the method of obtaining readings should be altered accordingly. After making the water and liquid columns to be stationary adjust the tips of the indexes to touch the water and liquid surfaces in the beakers. Measure height hw′h_{w}^{\prime} of the water column and the height hl′h_{l}^{\prime} of the liquid column from the tip of each index.
3
  • If ρw\rho_{w} and ρl\rho_{l} are the densities of water and liquid respectively, p0p_{0} the atmospheric pressure, and pp the pressure of the air in the tube,
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p_{a}=p+(h_{w}^{\prime}+x_{1})\rho_{w}g=p+(h_{l}^{\prime}+x_{2})\rho_{l}g

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(h_{w}^{\prime}+x_{1})\rho_{w}=(h_{l}^{\prime}+x_{2})\rho_{l}

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h_{w}^{\prime}=(\frac{\rho_{l}}{\rho_{w}})h_{l}^{\prime}+\frac{1}{\rho_{w}}(x_{2}\rho_{l}-x_{1}\rho_{w})

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  • Gradient of the graph hw′h_{w}^{\prime} against hl′=ρlρw=h_{l}^{\prime} = \frac{\rho_{l}}{\rho_{w}} = relative density of the liquid.

Past Paper Questions

Q1

Hare's Apparatus and Relative Density 2018

2018 • GCE Advanced Level • medium