11.5_ equilibrium calculations – chemistry libretexts

The six Problem Examples presented above were carefully selected to span the range of problem types that students enrolled in first-year college chemistry courses are expected to be able to deal with. Military diet alternatives If you are able to reproduce these solutions on your own, you should be well prepared on this topic.

• The first step in the solution of all but the simplest equilibrium problems is to sketch out a table showing for each component the initial concentration or pressure, the change in this quantity (for example, +2 x), and the equilibrium values (for example, .0036 + 2 x). Losing weight after 60 In doing so, the sequence of calculations required to get to the answer usually becomes apparent.

• Equilibrium calculations often involve quadratic- or higher-order equations. Weight loss pills side effects Because concentrations, pressures, and equilibrium constants are seldom known to a precision of more than a few significant figures, there is no need to seek exact solutions.


How to lose weight fast and healthy Iterative approximations (as in Problem Example 3) or use of a graphical calculator (Problem Example 4) are adequate and convenient.

• Phase distribution equilibria play an important role in chemical separation processes on both laboratory and industrial scales. Exercise synonym They are also involved in the movement of chemicals between different parts of the environment, and in the bioconcentration of pollutants in the food chain.

This page presents examples that cover most of the kinds of equilibrium problems you are likely to encounter in a first-year university course. Exercise workouts for legs Reading this page will not teach you how to work equilibrium problems! The only one who can teach you how to interpret, understand, and solve problems is yourself. So don’t just “read” this and think you are finished. Weight loss 4 texas You need to find and solve similar problems on your own. How to lose weight in 7 days naturally Look over the problems in your homework assignment or at the end of the appropriate chapter in a textbook, and see how they fit into the general types described below. Paleo english muffin When you can solve them without looking at the examples below, you will be well on your way!

Clearly, if the concentrations or pressures of all the components of a reaction are known, then the value of K can be found by simple substitution. Diet plan application Observing individual concentrations or partial pressures directly may be not always be practical, however. Low carb diet and exercise If one of the components is colored, the extent to which it absorbs light of an appropriate wavelength may serve as an index of its concentration. Low carb diet depression Pressure measurements are ordinarily able to measure only the total pressure of a gaseous mixture, so if two or more gaseous products are present in the equilibrium mixture, the partial pressure of one may need to be inferred from that of the other, taking into account the stoichiometry of the reaction.

No explicit molar concentrations are given, but we do know that for every n moles of HI, 0.223 n moles of each product is formed and (1–0.233) n = 0.777 n moles of HI remains. Weight loss images simulator free For simplicity, we assume that n=1 and that the reaction is carried out in a 1.00-L vessel, so that we can substitute the required concentration terms directly into the equilibrium expression.

\[K_c = \dfrac{[H_2][I_2]}{[HI]^2} = \dfrac{(0.233)^2}{(0.777)^2} = 0.12
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Example \(\PageIndex{2}\): Evaluating the Equilibrium Constant

Ordinary white phosphorus, P 4, forms a vapor which dissociates into diatomic molecules at high temperatures:

A sample of white phosphorus, when heated to 1000°C, formed a vapor having a total pressure of 0.20 atm and a density of 0.152 g L –1. Causes of weight loss in elderly Use this information to evaluate the equilibrium constant \(K_p\) for this reaction.

Before worrying about what the density of the gas mixture has to do with \(K_p\) , start out in the usual way by laying out the information required to express K p in terms of an unknown x ICE Table

Since \(K\) is independent of the number of moles, assume the simplest initial case.

\(p_{P_4} = \chi_{P_4} 0.2 = \left( \dfrac{1-x}{1+x}ight) 0.2 \)

\(p_{P_2} = \chi_{P_2} 0.2 = \left( \dfrac{2x}{1+x}ight) 0.2 \)

Partial pressure is the mole fraction times the total pressure.

The partial pressures in the bottom row were found by multiplying the mole fraction of each gas by the total pressure:

with the term in the denominator of each mole fraction is the total number of moles of gas present at equilibrium:

\[ K_p = \dfrac{p^2_{P_2}}{p_{P_4}} = \dfrac{\left(\frac{2x}{1+x}ight)^2 0.2^2} {\left(\frac{1-x}{1+x}ight) 0.2} = \left(\dfrac{4x^2}{(1-x)(1+x)}ight) 0.2
onumber\]

Now we need to find the dissociation fraction \(x\) of \(P_4\), and at this point we hope you remember those gas laws that you were told you would be needing later in the course! The density of a gas is directly proportional to its molecular weight, so you need to calculate the densities of pure \(P_4\) and pure \(P_2\) vapors under the conditions of the experiment. Best diet app One of these densities will be greater than 0.152 gL –1 and the other will be smaller; all you need to do is to find where the measured density falls in between the two limits, and you will have the dissociation fraction.

The molecular weight of phosphorus is 31.97, giving a molar mass of 127.9 g for P 4. Fastest way to lose weight This mass must be divided by the volume to find the density; assuming ideal gas behavior, the volume of 127.9 g (1 mole) of P 4 is given by RT/P, which works out to 522 L (remember to use the absolute temperature here.) The density of pure P 4 vapor under the conditions of the experiment is then

This is by far the most common kind of equilibrium problem you will encounter: starting with an arbitrary number of moles of each component, how many moles of each will be present when the system comes to equilibrium? The principal source of confusion and error for beginners relates to the need to determine the values of several unknowns (a concentration or pressure for each component) from a single equation, the equilibrium expression. Weight loss green smoothie The key to this is to make use of the stoichiometric relationships between the various components, which usually allow us to express the equilibrium composition in terms of a single variable. Exercise routine for women The easiest and most error-free way of doing this is adopt a systematic approach in which you create and fill in a small table as shown in the following problem example. Lose belly fat overnight You then substitute the equilibrium values into the equilibrium constant expression, and solve it for the unknown.

This very often involves solving a quadratic or higher-order equation. Healthy diet in pregnancy Quadratics can of course be solved by using the familiar quadratic formula, but it is often easier to use an algebraic or graphical approximation, and for higher-order equations this is the only practical approach. Low carb diet for weight loss There is almost never any need to get an exact answer, since the equilibrium constants you start with are rarely known all that precisely anyway.

Phosgene (\(COCl_2\)) is a poisonous gas that dissociates at high temperature into two other poisonous gases, carbon monoxide and chlorine. Paleo honey mustard The equilibrium constant K p = 0.0041 at 600°K. Weight loss yoga poses Find the equilibrium composition of the system after 0.124 atm of COCl 2 is allowed to reach equilibrium at this temperature.

Start by drawing up a table showing the relationships between the components: ICE Table

This expression can be rearranged into standard polynomial form

and solved by the quadratic formula, but we will simply obtain an approximate solution by iteration. I want to lose weight fast Because the equilibrium constant is small, we know that x will be rather small compared to 0.124, so the above relation can be approximated by

and x = 0.0206 which is sufficiently close to the previous to be considered the final result. Weight loss unexplained The final partial pressures are then 0.104 atm for COCl 2, and 0.0206 atm each for CO and Cl 2.

Comment: Using the quadratic formula to find the exact solution yields the two roots –0.0247 (which we ignore) and 0.0206, which show that our approximation is quite good.

What will be the partial pressures of all three components if 0.200 mole of PCl 5 and 3.00 moles of PCl 3 are combined and brought to equilibrium at this temperature and at a total pressure of 1.00 atm?

As always, set up a table showing what you know (first two rows) and then expressing the equilibrium quantities: ICE Table

The partial pressures in the bottom row were found by multiplying the mole fraction of each gas by the total pressure:

with the term in the denominator of each mole fraction is the total number of moles of gas present at equilibrium:

Substituting the equilibrium partial pressures into the equilibrium expression, we have

\[CH_3COOH_{(l)} + C_2H_5OH_{(l)} ightleftharpoons CH_3COOC_2H_{5(l)} + H_2O_{(l)} \]

(in which the water concentration does change), dilution will have no effect on the equilibrium; the situation is analogous to the way the pressure dependence of a gas-phase reaction depends on the number of moles of gaseous components on either side of the equation.

It often happens that two immiscible liquid phases are in contact, one of which contains a solute. Weight loss recipes for dinner How will the solute tend to distribute itself between the two phases? One’s first thought might be that some of the solute will migrate from one phase into the other until it is distributed equally between the two phases, since this would correspond to the maximum dispersion (randomness) of the solute. Snacks for low carb diet This, however, does not take into the account the differing solubilities the solute might have in the two liquids; if such a difference does exist, the solute will preferentially migrate into the phase in which it is more soluble.

For a solute S distributed between two phases a and b the process S a = S bis defined by the distribution law

• K a ,b is the distribution ratio (also called the distribution coefficient) and

The transport of substances between different phases is of immense importance in such diverse fields as pharmacology and environmental science. Weight loss yoga with adriene For example, if a drug is to pass from the aqueous phase with the stomach into the bloodstream, it must pass through the lipid (oil-like) phase of the epithelial cells that line the digestive tract. Exercise pictures with quotes Similarly, a pollutant such as a pesticide residue that is more soluble in oil than in water will be preferentially taken up and retained by marine organism, especially fish, whose bodies contain more oil-like substances; this is basically the mechanism whereby such residues as DDT can undergo biomagnification as they become more concentrated at higher levels within the food chain. How to lose weight naturally and fast For this reason, environmental regulations now require that oil-water distribution ratios be established for any new chemical likely to find its way into natural waters. Weight loss tips for teens The standard “oil” phase that is almost universally used is octanol, C 8H 17OH.

In preparative chemistry it is frequently necessary to recover a desired product present in a reaction mixture by extracting it into another liquid in which it is more soluble than the unwanted substances. Exercise at home without weights On the laboratory scale this operation is carried out in a separatory funnel as shown below. Paleo diet crossfit The two immiscible liquids are poured into the funnel through the opening at the top. Diet plan to lose belly fat in 2 weeks The funnel is then shaken to bring the two phases into intimate contact, and then set aside to allow the two liquids to separate into layers, which are then separated by allowing the more dense liquid to exit through the stopcock at the bottom.

If the distribution ratio is too low to achieve efficient separation in a single step, it can be repeated; there are automated devices that can carry out hundreds of successive extractions, each yielding a product of higher purity. Liquid diet for weight loss results In these applications our goal is to exploit the Le Chatelier principle by repeatedly upsetting the phase distribution equilibrium that would result if two phases were to remain in permanent contact.

The distribution ratio for iodine between water and carbon disulfide is 650. Lose weight fast without exercise in 7 days Calculate the concentration of I 2 remaining in the aqueous phase after 50.0 mL of 0.10M I 2 in water is shaken with 10.0 mL of CS 2.

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