Solubility of Solids and Gases; Henry's Law

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle first. The air around us is about twenty one percent oxygen, by moles. Some of this air dissolves in water. In that dissolved air, what percentage is oxygen? Twenty one again, surely? Not quite! By the end of this lesson, you will work it out yourself. This is Henry's law, and it comes up often in JEE, so let's begin.

0:27Solubility: how much can dissolve?

So, first, solubility. Keep adding salt to water, and after a point, the extra just sits at the bottom. That limit is the solubility: the maximum amount that dissolves in a given amount of solvent, at a given temperature, the capital T on screen. Okay? The solution at that limit is saturated. It is in dynamic equilibrium with the undissolved solute: salt keeps dissolving and coming back out, at the same rate.

0:56Solids in liquids: Le Chatelier decides

Right? Now, for a solid dissolving in a liquid, pressure has almost no effect. Temperature decides. Suppose dissolving absorbs heat, and remember, the saturated solution is an equilibrium. So if you heat it, does more solid dissolve, or less? More, exactly! Le Chatelier's principle: add heat, and the equilibrium shifts the way that absorbs heat, so solubility rises with temperature. This dissolving is endothermic: delta sol H, the enthalpy of solution, is greater than zero. Delta is the little triangle, with sol, for solution, in the subscript. Examples: ammonium chloride, N H four C l, and potassium nitrate, KNO three. With me? So, hot water always dissolves more of any solid, right? No, no, careful! If dissolving gives out heat, it is exothermic: delta sol H is less than zero, and heating lowers the solubility. Example: cerium sulphate, C e two, then S O four in brackets, taken three times. Got it?

2:03Gases in liquids: Henry's law

Now gases in liquids. Henry's law: at constant temperature, the solubility of a gas is proportional to its partial pressure above the liquid. This sign, like an open alpha, means proportional to. Quick check: a gas dissolves zero point zero six six grams per litre at one bar. At five bar, same temperature? Yes! Five times the pressure, five times the solubility: zero point three three grams per litre. The g L to the power minus one means grams per litre, and the double arrow means so. Easy, right? Now the mole-fraction form, the one we use in numericals: p equals K H, that is K with the subscript H, times x. Here p is the partial pressure of the gas. Okay? And x is the mole fraction of the gas in the solution, and K H is Henry's law constant. Mole fraction has no unit, so K H is a pressure: bar, or k bar, that is kilobar, a thousand bar. Clear?

3:07Reading KH: larger means less soluble

Now the graph: p goes up, x goes across. Since p equals K H times x, each gas is a straight line through the origin, with slope K H, okay? Gas one has the steeper line, so its K H is larger. Now, at the same pressure, which gas reaches the smaller x? Gas one, the steeper line, yes! Same p, larger K H, so a smaller x: less gas dissolved. Hence the label, less soluble. The larger the K H, the less soluble the gas. Write it down! Right? Now, dissolving a gas gives out heat. So, same idea as for solids: in warm water, does more gas dissolve, or less? Less, exactly! Heat pushes the gas out. In Henry's law language, K H rises with temperature. That is why fish struggle in warm water: less oxygen, O two, dissolves. With me?

4:07Henry's law in real life, and where it fails

Now, real life. Soda is sealed under high carbon dioxide pressure, C O two, so a lot of gas stays dissolved. Open it, the pressure drops, and the gas bubbles out: the fizz! Okay? Scuba divers breathe compressed air, so extra nitrogen, N two, dissolves in their blood. Rise too fast, and it forms bubbles: the bends. So their air is diluted with helium, which is less soluble. Clear? At high altitude, the partial pressure of oxygen is low, so less oxygen dissolves in the blood: anoxia. Right? Now, a trap. Ammonia is a gas that dissolves in water. So Henry's law works for it too, right? No, no, careful! Henry's law holds only for dilute solutions of gases that do not react with the solvent. Ammonia, N H three, and H C l react or ionise in water, so they deviate; so does carbon dioxide at very high pressure, the small p. Got it?

5:09Example 1: mole fraction of N2 dissolved in water

Now, Example one. Nitrogen at a partial pressure of zero point eight bar is in contact with water at two ninety three kelvin, and K H for nitrogen is seventy six point five kilobar. Find the mole fraction of nitrogen in the water, and the millimoles dissolved per litre. Pause the video, and try it first. Done? Okay, let's check. Henry's law gives x equals p over K H, okay? So x is zero point eight over seventy six point five, right? No, no, careful! K H is in kilobar, but p is in bar. One kilobar is one thousand bar, so K H is seventy six thousand five hundred bar. Miss this, and your answer is a thousand times too big. With me? So, x is zero point eight over seventy six thousand five hundred: one point zero five times ten to the power minus five. Tiny, as expected. Okay? Now a topper's trick. One litre of water, one thousand grams, at eighteen grams per mole, is about fifty five point five moles; the wavy equals sign means about. And x is so tiny that n, the moles of nitrogen, is about x times fifty five point five. Clear? So, n is one point zero five times ten to the power minus five, times fifty five point five: five point eight times ten to the power minus four moles. That is zero point five eight millimoles per litre. That's it!

6:42Example 2: mole percent of O2 in air dissolved in water

Now Example two: our puzzle. Air, twenty one percent oxygen and seventy nine percent nitrogen by moles, at one bar, is in equilibrium with water. K H is thirty four point nine kilobar for oxygen, and seventy six point five for nitrogen. Find the mole percentage of oxygen in the dissolved air. Pause and try. Hint: find each partial pressure first. Done? Okay, let's check. The total is one bar, so each partial pressure is that gas's share of it. p with the subscript O two, oxygen's partial pressure, is zero point two one bar; nitrogen's, zero point seven nine bar. Okay? For oxygen, K H in bar is thirty four thousand nine hundred. So x for oxygen is zero point two one over thirty four thousand nine hundred: six point zero two times ten to the power minus six. Right? For nitrogen: zero point seven nine over seventy six thousand five hundred, that is one point zero three times ten to the power minus five. Now, oxygen's K H is less than half of nitrogen's. So in the dissolved air, is oxygen's share above twenty one percent, or below? Above, yes! Oxygen is more soluble. Writing nitrogen's x as ten point three times ten to the power minus six, oxygen's share is six point zero two, over six point zero two plus ten point three: about zero point three seven, or thirty seven percent! Puzzle solved: air is twenty one percent oxygen, but dissolved air is about thirty seven percent. Lucky fish!

8:26Quick revision: solids, gases and p = KH x

So, quick revision. Solids: pressure hardly matters; temperature acts through delta sol H, okay? Gases: more pressure, more dissolves; warmer, less dissolves. And Henry's law: p equals K H times x; the larger the K H, the less soluble the gas. Now go and try the practice problems on this page. All the best!