Analysis

The graph below traces the location of sodium through each 1/30s frame. It is interesting to see how the sodium moves in the container. The sodium travels in relatively straight lines throughout the reaction. We hypothesize that immediately following the drop, one area on the sodium (most likely an area with less excess oil than other areas) reacts before the rest of the sodium. Therefore, this area would be the first location that created hydrogen gas. The hydrogen gas emissions acts as a propellant to move the sodium forward. The sodium hits a wall, and the collision changes its course of direction. As the sodium travels, it leaves behind a wake. The force of the sodium pushing the water in front of it causes the water in the wake behind it to have a lower pressure. This lower pressure region, along with eddies created by the movement of water, helps to mix the reactants (sodium and H₂O). The extra mixing allows even more hydrogen to be created behind the sodium, continuing to propel it in a straight line. Click on the link to see the actual clip for this graph: Sodium Bottom View 1 small. You might see in this clip that the sodium sometimes changes direction before actually hitting the side of the container. We think that this could be caused by the previous disruption of the water. As the sodium causes turbulence in the water, it becomes less likely that the hydrogen emission from the back of the sodium can be strongest. Therefore, hydrogen gas emissions in other parts of the sodium propel the sodium in a different direction. It is also possible that the turbulence of the water causes the sodium to turn around, so that the position of strong hydrogen emission is on the same area of the sodium, but it appears to be in a different location according to its relation to the container. Another clip that illustrates this concept very well is Sodium Top View small.

As you can see from the graph below and the clip it came from, Potassium Bottom View small, potassium also travels in a relatively straight line. We think that potassium is also propelled by hydrogen gas emissions that are concentrated in one area. The potassium reaction takes less time than the sodium reaction, consequently causing the potassium to travel a shorter distance, as you can tell from the graph, position of potassium. It also seems as though the potassium takes longer to begin moving in a straight line than sodium. The graph below shows that the potassium squiggled around before it began to move in a straight line. (The coordinates of the drop are approximately (450mm, 420mm).) This could be due to the time it takes for the water and potassium to react, allowing hydrogen gas to propel the potassium.

This graph shows the movement of lithium through the first 5th of clip Lithium Bottom View 2 small. Lithium does not create as much of a reaction as potassium or sodium, so it takes longer for the hydrogen gas to propel the lithium. The area of lithium that creates the hydrogen gas seems to be more randomly chosen than in potassium or sodium. The movement of lithium is not fast enough to create a wake that would ease the production of hydrogen in one area. Instead, hydrogen is created uniformly around the lithium. It is possible to watch the clip and determine which direction the lithium will move from seeing which side a hydrogen bubble appears.

Using Video Point and Excel, we calculated the average total velocities of each of the reactions. We did this by using the data coordinates of the metal at different points in the reaction. We found the distance between two points (since we had hundreds of data points to choose from we did 10 points throughout chosen from equal amounts of time apart). We calculated the distance that the metal had moved from the first frame chosen to the next frame. After we had computed the distance from the equation d²=x²+y²we computed the speed using the equation v = d/t. The speeds of the metals, based on our calculations, were determined to be:

Metal

Average Total Velocity (m/s)

Lithium

0.0044

Sodium

0.0143

Potassium

0.0495

As you can see, potassium moves the fastest in water, and lithium moves the slowest. You can see this in the clips that these values came from, Lithium Bottom View 2 small, Sodium Bottom View 1 small, and Potassium Bottom View small. It is probable that potassium and sodium move so much more quickly than lithium because they produce more hydrogen in their reactions. The hydrogen propels them, so more hydrogen ultimately means a greater velocity.

An unseen aspect of the reactions that is interesting to analyze is the amount of heat produced. The amount of heat that is created in each reaction is more or less important depending on the melting point of the metal in the reaction. Here are the melting points of the metals we used:

Metal	Melting Pt. (^o C)
Lithium	181
Sodium	98
Potassium	64

As you can see from this table, potassium, which has a lower melting point, would be more susceptible to higher temperatures than sodium or lithium. For example, if the heat in the reaction of potassium and water was 70 degrees Celsius, the potassium would melt. If the heat in the reaction of sodium and water was 70 degrees Celsius, however, the sodium would not melt.

From a CRC¹, we found the Heats of Fusion. Heat of Fusion is the amount of kilojoules that it takes to melt one mole of a substance. It is a way to translate melting point into energy/substance. Here are the Heats of Fusion of the metals we used:

Metal	Heat of Fusion (kJ/mol)
Lithium	2.99
Sodium	2.60
Potassium	2.33

It takes less energy for potassium to melt than sodium or lithium because the melting point for potassium is lower; it takes less heat for potassium to go from solid to liquid.

An interesting aspect of how these metals melt is the spherical form they take on. After speaking with Mr. Roser, we determined that the heat of the reaction causes the metals to take on their most defensive and stable form--a sphere. The lithium reactions we tried did not produce enough heat for the lithium to take on a spherical shape. If we had used greater amounts of lithium, it is possible that enough heat would have been created for the lithium to form a sphere similarly to the sodium and potassium.

The density of each of the metals is much less than that of water, which is why the metals are able to skid across the top of the water without sinking. To see the exact densities, visit our Theory page.