# Video: Identifying the Graph That Best Describes the Relationship between the Mass of Gas That Is Soluble in a Given Mass of Water and the Temperature for a Gas This Is Highly Soluble in a Set of Graphs

Which of the following graphs best shows the relationship between the number of grams of a gas that are soluble in 50 grams of H₂O and the temperature of the water, if the solubility begins at a high value? [A] Graph A [B] Graph B [C] Graph C [D] Graph D [E] Graph E

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### Video Transcript

Which of the following graphs best shows the relationship between the number of grams of a gas that are soluble in 50 grams of H₂O and the temperature of the water, if the solubility begins at a high value? And we’ve been given five different graphs with five different shapes of plot.

Solubility is the measure of how much solute will dissolve in a solvent to achieve a saturated solution. Commonly, the units for solubility are grams of solute per 100 mL of solvent or milligrams of solute per 100 mL of solvent. But in this case, the question indicates that our units would be grams of gas per 50 grams of H₂O. Although since we’re only looking for a general shape of the relationship, the units don’t matter a great deal. What we’re looking for is the general shape of the relationship between solubility and temperature.

Because the solubility was mentioned first and it’s the thing that we would measure, that’s the dependent variable. And the temperature, since it’s mentioned second, we assume is our independent variable. It’s very straightforward to change the temperature of a solution and then measure the solubility. So our solubility goes on the 𝑦-axis and our temperature goes on the 𝑥-axis. We know that, at about zero degrees, our solution will freeze and, about 100 degrees, our solution will boil. So we can only usefully define the solubility of our gas in water in this temperature range.

The question says that our solubility begins at a high value. So I’m putting an 𝑥 roughly in the middle at the starting point of our solubility curve to the far left, where our solution would be about to freeze. This way, I have room to move above and below depending on what the relationship works out to be. We can quickly dismiss A and D because they start at low values. A starting value for E isn’t particularly high, but I’ll hold on to it just in case.

Now, let’s have a look at the solution at the starting temperature. We have plenty of gas particles in our solution because the solubility starts at a high value. As we heat up the solution, the stuff that’s dissolved is going to move around much faster. When these particles eventually reach the surface of the solution, they’re likely to escape. Since they’re gas particles, they won’t be sticking to each other or to the water especially strongly. So they’ll simply escape. If we try to add any more to the solution, they’ll escape just as fast.

So, generally speaking, the solubility of a gas will go down as the temperature increases. This is because as we’re adding energy, we’re making it easier for the gas to escape. But we’re not making it easier for the gas to come back. So overall, it means less gas can stay in the liquid at one time. In graph B, the plot is staying perfectly level, indicating that the solubility is constant with respect to temperature. And in graph E, the plot suggests that solubility increases as temperature increases. So neither B or E can be correct answers.

What we do tend to see is that the most dramatic decreases in solubility occur at the start. And less dramatic decreases occur as we increase the temperature by the same amount. This reflects the shape we see in graph C. When the temperature is low, the solubility is high. When the temperature is high, the solubility is low. And a smooth curve connects these points.

So the graph that best shows the relationship between the number of grams of a gas that are soluble in 50 grams of H₂O and the temperature of the water if the solubility begins at a high value is C.