To find the density of a solid that dissolves in water, direct water displacement methods (like Archimedes' principle using water) cannot be used because the solid would dissolve. Instead, specialized techniques are employed to determine its density.
Determining the Density of the Solid Itself
The density of any solid is defined as its mass per unit volume ($ \text{Density} = \text{Mass} / \text{Volume} $). For water-soluble solids, the challenge lies in accurately measuring the volume of the solid without it dissolving.
Method 1: Using an Immiscible Liquid
This is the most common and practical method. An immiscible liquid is one that does not mix with or dissolve the solid. For water-soluble solids, common choices for immiscible liquids include kerosene, mineral oil, or certain organic solvents, provided they do not react with the solid.
- Measure the Mass of the Solid: Use a digital balance to accurately determine the mass ($ \text{m}_{\text{solid}} $) of the solid sample.
- Select an Immiscible Liquid: Choose a liquid in which the solid is insoluble and that has a lower density than the solid itself, allowing the solid to sink.
- Measure the Volume of the Immiscible Liquid: Pour a known volume ($ \text{V}_{\text{liquid}} $) of the chosen immiscible liquid into a graduated cylinder.
- Add the Solid: Carefully add the solid sample to the graduated cylinder containing the immiscible liquid. Ensure no air bubbles are trapped with the solid. The solid will sink, and the liquid level will rise.
- Measure the New Volume: Read the new total volume ($ \text{V}_{\text{total}} $) of the liquid and solid.
- Calculate the Volume of the Solid: Subtract the initial volume of the liquid from the total volume: $ \text{V}{\text{solid}} = \text{V}{\text{total}} - \text{V}_{\text{liquid}} $.
- Calculate the Density of the Solid: Divide the mass of the solid by its calculated volume: $ \text{Density}{\text{solid}} = \text{m}{\text{solid}} / \text{V}_{\text{solid}} $.
For more details on density measurement techniques, you can refer to resources like ThoughtCo's explanation of density.
Method 2: Using a Pycnometer or Density Bottle
A pycnometer (or density bottle) is a small, precisely manufactured flask used for accurate density measurements, particularly for liquids and fine powders.
- Measure Mass of Empty Pycnometer: Weigh the clean, dry pycnometer ($ \text{m}_{\text{pyc}} $).
- Weigh Pycnometer with Immiscible Liquid: Fill the pycnometer with the chosen immiscible liquid (as described in Method 1), ensuring it's completely filled and free of air bubbles. Weigh it ($ \text{m}_{\text{pyc+liquid}} $).
- Determine Volume of Pycnometer: Calculate the mass of the liquid ($ \text{m}{\text{liquid}} = \text{m}{\text{pyc+liquid}} - \text{m}{\text{pyc}} $). Using the known density of the immiscible liquid ($ \text{Density}{\text{liquid}} $), calculate the volume of the pycnometer: $ \text{V}{\text{pyc}} = \text{m}{\text{liquid}} / \text{Density}_{\text{liquid}} $.
- Add the Solid to Pycnometer: Place a known mass of the solid ($ \text{m}_{\text{solid}} $) into the clean, dry pycnometer.
- Fill with Immiscible Liquid and Weigh: Carefully fill the pycnometer containing the solid with the immiscible liquid, ensuring no air bubbles. Weigh it ($ \text{m}_{\text{pyc+solid+liquid}} $).
- Calculate the Volume of Displaced Liquid:
- Mass of solid + liquid in pycnometer = $ \text{m}{\text{pyc+solid+liquid}} - \text{m}{\text{pyc}} $
- Mass of liquid only in pycnometer (if no solid) = $ \text{m}_{\text{liquid}} $ (from step 3)
- The difference in mass, plus the solid's mass, helps determine the volume of the solid. Specifically, the mass of the liquid that would fill the pycnometer if the solid weren't there is $ \text{m}{\text{liquid}} $. The mass of the liquid actually present with the solid is $ \text{m}{\text{pyc+solid+liquid}} - \text{m}{\text{pyc}} - \text{m}{\text{solid}} $.
- The mass of liquid displaced by the solid = $ \text{m}{\text{liquid}} - (\text{m}{\text{pyc+solid+liquid}} - \text{m}{\text{pyc}} - \text{m}{\text{solid}}) $.
- From this displaced mass and the liquid's density, calculate $ \text{V}_{\text{solid}} $.
- Calculate the Density of the Solid: $ \text{Density}{\text{solid}} = \text{m}{\text{solid}} / \text{V}_{\text{solid}} $.
Understanding Solution Density when a Solid Dissolves
While determining the density of the solid itself requires specific methods, it's also important to understand how the density of the solution changes when a water-soluble solid dissolves.
When a solid dissolves in water, the volume of the resulting solution often does not change appreciably from the initial volume of the water, especially for moderate concentrations. This phenomenon allows us to calculate the solution's density based on the added mass. For example, if you add 'X' grams of a solid to 1 liter (1000 ml) of water, the total mass of the solution becomes (1000 + X) grams. Assuming the volume remains approximately 1000 ml, the density of the solution can be calculated as:
$$ \text{Density of Solution} = \frac{\text{Total Mass of Solution}}{\text{Approximate Volume of Solution}} = \frac{1000 \text{ gm (water)} + X \text{ gm (solid)}}{1000 \text{ ml (approx. solution volume)}} $$
This can be expressed as (1000 + X) / 1000 kg/l or gm/ml.
Example Calculation of Solution Density:
| Solute Mass (X gm) | Water Volume (ml) | Total Solution Mass (gm) | Approximate Solution Volume (ml) | Solution Density (gm/ml) |
|---|---|---|---|---|
| 50 | 1000 | 1050 | 1000 | 1.05 |
| 100 | 1000 | 1100 | 1000 | 1.10 |
| 200 | 1000 | 1200 | 1000 | 1.20 |
Why is this important?
Understanding both the intrinsic density of a soluble solid and the density of the solutions it forms has several practical applications:
- Quality Control: Verifying the purity and identity of a solid.
- Concentration Determination: Solution density can be used to quickly estimate the concentration of a dissolved substance, especially in industrial processes.
- Formulation Science: Essential for formulating solutions in industries like pharmaceuticals, food and beverage, and chemistry.
- Separation Processes: Understanding density differences is crucial for separation techniques.
Important Considerations
- Temperature: Density is temperature-dependent. Ensure all measurements are taken at a consistent temperature.
- Purity of Solid: Impurities can affect the measured density.
- Accuracy of Measurements: Precision in mass and volume measurements is critical for accurate density determination.
- Nature of Immiscible Liquid: The chosen immiscible liquid must genuinely not dissolve or react with the solid.
