The aim of this experiment was to use different methods to calculate the relative density of the unknown solids and to identify them. When using the Hydrostatic Balance the relative densities calculated for the four solids were 9.1 ± 0.3, 9.2 ± 0.3, 8.7 ± 0.3 and 8.3 ± 0.3 which were found to be bronze, copper, silver and cobalt respectively. The Relative Density bottle was used to identify the relative densities of the metal shots, 11.1 ± 0.1, which suggests that is was Lead. Hare’s Apparatus was used to find the relative density of ethanol by measuring the heights of the liquid columns corresponding the ethanol and water, it was found to be 0.8 ± 0.01.

 

 Introduction

Calculating the relative densities of the unknown object has real-life applications such as finding if jewellery is made up of pure gold, which does not contain other elements such as lead. This can be calculated by finding the volume of the water displaced as we know that the density of gold is 19g/cm3 and the mass of gold, using equation 1. If the volume of water displaced is the same or similar to the theoretical value then the jewellery is made of pure gold. This is important so that there is a way of identifying jewellery that is worth more. Relative density gives a “better understanding of the quality of the substance” and also tells us if a certain substance will float or sink on water which is useful when it comes to manufacturing heavy objects such as ships 2. 

 

 Theory

Relative density is calculated through the ratio between the density of the substance ( ) and the density of water ( ) 3.

RDx =                           (equation 1)

       =         (equation 2)

Equation 2 can be derived from equation 1 when the weight is suspended in air and in water.

The Hydrostatic Balance method practises the Archimedes’ Principle which suggests that the weight of an object in water is equal to the magnitude of the upward/buoyant force 4. The volume of the water increases by the volume of the object regardless of its shape. The heavier the object acting on the water, the more water it is displacing. For instance, a heavier ship would have more force acting on it downwards due to the increased mass so the magnitude of the buoyant force is also increasing as it displaces more water. The Hydrostatic Balance method suggests that if the same object was placed in two different fluids, the weight of the object would be less in the fluid that is denser 3. If the relative density is more than 1 in water will sink and if the relative density is less than 1 the object will float. Relative density is constant but only under given conditions, if the pressure/temperature change the relative densities may change 5.

 

“The relative density bottle is a small flask” that allows the same volume of solution to be measured each time when the stopper is placed on it, as excess solution flow out 3.This is useful as it reduces the likelihood of the same volume not being used each time

The equation to find the relative density is below:

RDx =        (equation 3)

 

Ws = weight of shot pellets

Wb = weight of dry bottle

Wbw = weight of bottle with distilled water

Wbsw = weight of bottle with water and shot pellets

Wbs = weight of bottle with shot pellets

 

Hare’s apparatus is a “Y-shaped piece of glass tubing” which is used to find the relative density of ethanol by measuring the heights of the liquid columns corresponding to the beakers filled with ethanol and water.

The pressure on the surface of the water is below where P0 is the atmospheric pressure, w is the density of water, e is the density of water, w is the height travelled by water, g is the force of gravity and e is the height travelled by ethanol.

P0 – wg w            (equation 4)

The pressure on the surface of the water is the same as the pressure on the surface of ethanol which is defined as 3:

P0 – eg e                  (equation 5)

To calculate the relative density of ethanol:

RDethanol =         (equation 6)

 

Experimental Method

The three experiments used were The Hydrostatic Balance, The Relative Density Bottle and Hare’s Apparatus.

To carry out The Hydrostatic Balance set up the equipment in reference to figure 1, this is to measure the mass of the metal cylinder in the air. Then place the solid in a 250 ml beaker (Labline) of distilled water so that it is fully submerged 6. Make sure that the metal cylinder is not touching the beaker and that there are no air bubbles 3. Measure the mass of the metal cylinder using an electronic balance to give the value of the solid in distilled water. Repeat the same procedure using a salt solution which can be created by adding salt to distilled water. Follow the same steps for the other three metal cylinders’.

                           

Figure 1: A sketch to show how the Hydrostatic balance is used to measure the relative density of water/ salt solution.

The Relative Density bottle is used to identify the relative densities of the salt solution and the metal shots. The relative density bottle allows the same volume of solution to be measured each time when the stopper is placed on it, as excess solution flow out 6. First, obtain the mass of the dry empty bottle (from Trishakti Scientific Company 7), using the weighing scales. Fill the bottle to the top using salt solution so that any excess flows out and weight it. Repeat steps substituting salt solution with distilled water. Obtain 50g of the shot pellets and add it to the bottle with distilled water and swipe of the excess and measure the total mass. To find the relative density of the metal shots, you add a known value of the metal shots to the bottle filled with distilled water and measure the volume of the water displaced.  

Figure 2: A sketch of the relative density bottle where the solutions/ pellets are added

Hare’s Apparatus is used to find the relative density of ethanol. Make sure the apparatus is clean so that it eliminates any contamination. Obtain 2 50ml beakers of the same size and fill each beaker with 30ml of Ethanol and distilled into each beaker, using a measuring cylinder. Place the ends of the tubes into each beaker. Suck using the third tube so that both the liquids rise 3. Then measure the height from the top of the solution in the beaker o the meniscus in the tube for each solution.

 

 

 

Figure 3: A sketch to show Hare’s Apparatus in order to find the relative density of other ethanol

 

Results

The Hydrostatic Balance:

Metal Cylinder

Mass in air (g)

Mass in water       (g)

Bronze

15.5

13.8

Copper

16.6

14.8

Silver

16.6

13.8

Cobalt

14.9

13.1

 

?E =         ?E = ±0.3

From the results, there is a clear pattern that when the same object was placed in two different fluids, whilst keeping variables such as temperature constant, the mass of the object would be less in the fluid that is denser. For instance, the mass of bronze was 15.5g in air but only 13.8g in water which indicates that water is denser than air.

Weight of mass in salt solution =9.06

Weight of mass in air =6.16

By using equation 1 the relative density of salt can be calculated. 

RDsalt =      =1.47   (equation 1)

 

The Relative Density Bottle:

Ws = 34.7g                              

 Wbw = 83.6g

Wbs = 85.5      

Wbsalt = 84.6g

Shot pellets = 50g                

Wbsw = 129.9g

Balance precision=0.1g    Error=  ± 0.05g

 

RDpellet =       =11.1             (equation 3)

Error=                 = 0.01

?E = 11.1± 0.01

 

The standard relative density of lead is 11.37 which is close to the value calculated from the experiment, 11.1. This shows that the experiment is reliable as similar results were obtained.

Hare’s Apparatus:

Height of ethanol (he): 5.8cm

Height of distilled water (hw): 4.9cm    

RD =        = 0.85             (equation 6)

?E=         = 0.01

RDE = 0.85 ± 0.01

The standard relative density of ethanol is 0.789; this is close to the calculated value from the experiment.

 

Discussion

The Hydrostatic Balance:

The main error of this experiment is the balance. This is because the balance only gave measurements 2 d.p. The temperature could have also affected the relative density. However, the results are reliable as they are consistent and are similar to the standard relative densities. This method is good for substances denser than water.

The Hydrostatic Balance method suggests that if the same object was placed in two different fluids, whilst keeping variables such as temperature constant, the weight of the object would be less in the fluid that is denser 3. This is supported by my results, the weight of A was 15.4g in the air but in water, it was 13.7g and in a salt solution is was 12.9g. This supports the theory that if the same object was placed in two different fluids, whilst keeping variables such as temperature constant, the weight of the object would be less in the fluid that is denser. The salt solution is denser than water and air, therefore, the mass of the metal cylinder is far less.

The Relative Density Bottle:

The errors in this experiment could be the temperature of the bottle used as it was not completely dry or clean when being used. Also, there could have been an excess solution in the bottle from the previous experiment which may have affected the outcome. This method is useful for measuring the relative densities of liquids as solids cannot travel up the tube unless it is molten or dissolved in a solution.

Hare’s Apparatus:

One of the main errors was the reading error from the ruler as it can be difficult to position the ruler on the solution in the beaker and read it from the meniscus in the tube. The results obtained are similar to the standard value. To improve this experiment, the apparatus should be thoroughly cleaned and when measuring the height of the distance travelled by the liquid, keep the ruler still. This method is used for liquids.

 

Conclusions

The main aim of the experiment was to use 3 different methods to calculate the relative densities of substances. The results obtained from the first experiment supported Archimedes’ Principle as the mass decreased as the density increased which shows that there is a negative correlation between the two variables. The second experiment allowed an unknown substance to be calculated through finding its relative density and comparing it to known variable, which was discovered to be Lead. Hare’s Apparatus calculated the relative density of ethanol by comparing the height travelled to water. All these experiments follow different ways of calculating relative densities for substances of different states which is useful as it allows researchers to use two methods and see if they get similar results in both methods to check if their results are reliable.

 

References

1 http://www.scienceclarified.com/everyday/Real-Life-Chemistry-Vol-3-Physics-Vol-1/Density-and-Volume-Real-life-applications.html

2 https://socratic.org/questions/name-two-advantages-of-relative-density-over-density-in-measurement

3 Physics lab book

4 https://www.britannica.com/science/Archimedes-principle

5 https://www.youtube.com/watch?v=omRMpPYh_vw

6 https://dir.indiamart.com/impcat/glass-beakers.html

7 https://www.indiamart.com/proddetail/lab-bottle-relative-density-6921794997.html