EjerciciosFyQ

Calculation of equilibrium constants and degree of dissociation of N2O4 (8413)

F_y_Q — 2025-03-14T05:49:47Z

At and 1 atm, dissociates into by according to the following equilibrium:

2NO2(g)}" title="\ce{N2O4(g) <=> 2NO2(g)}" />

Calculate:

a) The values of the equilibrium constants and at this temperature.

b) The percentage of dissociation at and a total pressure of 0.1 atm.

Data: .

The first step is to determine the number of moles of each substance at equilibrium, based on the initial moles and the degree of dissociation ():

\underset{2n_0\alpha}{\ce{2NO2(g)}}}" title="\ce{\underset{n_0(1-\alpha)}{\ce{N2O4(g)}}} \ce{<=> \underset{2n_0\alpha}{\ce{2NO2(g)}}}" />

Since the degree of dissociation is , the moles can be written as:

\underset{0.4n_0}{\ce{2NO2(g)}}}" title="\ce{\underset{0.8n_0}{\ce{N2O4(g)}}} \ce{<=> \underset{0.4n_0}{\ce{2NO2(g)}}}" />

The total number of moles at equilibrium is the sum of all species:

Next, calculate the mole fraction for each substance:

a) The equilibrium constant in terms of partial pressures is:

Substitute the values into this equation to determine the constant:

The equilibrium constant in terms of concentrations is calculated as:

The change in the number of moles of gas is one, so substitute the values to find the constant:

b) When the total pressure of the system changes to 0.1 amt, the equilibrium shifts to favor greater dissociation of . The same expression for holds, and it is used to calculate the new degree of dissociation under these conditions. Be cautious to express the mole fractions in terms of the initial moles:

For simplicity, work with the denominator and substitute to make solving easier:

pH and pOH of an acetic acid solution (8401)

F_y_Q — 2025-02-17T05:12:03Z

Calculate the pH and pOH of a 0.001 mol/L acetic acid solution, given its ionization constant

From the ionization constant value, you can calculate the concentration of ions at equilibrium:

CH3COO^- + H3O^+}}}" title="\color[RGB]{2,112,20}{\textbf{\ce{CH3COOH + H2O <=> CH3COO^- + H3O^+}}}" />

The acidity constant follows the equation:

The equilibrium concentrations, based on the initial concentration, are as follows:

Substitute these concentrations into the equilibrium constant equation to get:

You can do one of two things: solve the quadratic equation or assume that, given the small value of the constant, the denominator is very close to one. Here's how to do each.

Solving the quadratic equation:

You get the value . The other value obtained is negative and lacks chemical significance.

Approximating the denominator as one:

Since the acid concentration is low, it's not a good idea to use the approximation, and it is preferable to solve the quadratic equation to avoid an error of over .

Taking the first calculated dissociation degree value, you can calculate the equilibrium hydronium concentration:

The pH calculation is straightforward:

You can calculate the pOH considering their relationship:

Relationship between molarity and normality (8380)

F_y_Q — 2025-01-27T04:52:56Z

Calculate the normality of the following solutions: a) (2 M) b) (0.4 M) c) (3 M) d) (1 M) e) (2 M)

Normality is defined as the number of equivalents of solute in one liter of solution. The mass of an equivalent is the molecular mass divided by the number of "H" or "OH" groups in the acid or base considered. This means that the relationship between normality and molarity is that normality is equal to molarity multiplied by the number of "H" or "OH" groups in the species.

a)

b)

c)

d)

e) (because it is a salt with a 1:1 stoichiometry between its ions).

Force a man must exert to pull a sled (8334)

F_y_Q — 2024-10-23T03:01:15Z

A man pulls a sled up a ramp using a rope attached to the front, as illustrated in the figure.

The sled has a mass of 80 kg. The kinetic friction coefficient between the sled and the ramp is (), the angle between the ramp and the horizontal is , and the angle between the rope and the ramp is . What force must the man exert to keep the sled moving at a constant speed?

To analyze the forces acting on the sled, decompose them according to the system formed by the direction of movement and a perpendicular axis:

The components of the weight and applied force are:

In the direction perpendicular to the ramp, the sum of the forces must be zero. Consider the "y-component" of the weight to solve for the normal force:

In the direction of movement, the sum of the forces must also be zero because the sled moves at a constant speed. This gives:

The friction force is the product of the normal force and the coefficient of friction:

Substitute the known values into the equations to solve for the force exerted by the man:

Acceleration and time taken by a car to increase speed (8329)

F_y_Q — 2024-10-10T03:34:15Z

A car, which has uniformly accelerated motion, increases its speed from 18 km/h to 72 km/h over a straight distance of 37.5 meters. Calculate the time taken for this journey and its acceleration.

To make the problem homogeneous, the first step is to express the speeds in SI units:

You can relate the change in speed and the distance covered with the car's acceleration:

Substitute the values and calculate:

The time needed to make this speed change is:

Substitute and calculate:

Kinetic energy of a moving projectile (8317)

F_y_Q — 2024-09-19T04:20:43Z

Calculate the kinetic energy of an 18 g projectile moving horizontally at .

If you observe the units in the problem statement, you will see that the mass is not expressed in the SI unit of mass. The first thing you need to do is convert it to kg to make the problem homogeneous.

The kinetic energy of the projectile is given by the equation:

You know the necessary data, so you just need to substitute and calculate:

General gas law (8316)

F_y_Q — 2024-09-17T02:52:07Z

Calculate the final temperature of a gas enclosed in a volume of 2 L at 1 atm, if we reduce its volume to 0.5 L and its pressure increases to 3.8 atm.

You will use the state equation of gases:

Solving for the value of :

Calculation of braking acceleration (8312)

F_y_Q — 2024-09-16T03:46:33Z

Determine the acceleration of a car, initially moving at a speed of 120 km/h, knowing that it takes 20 seconds to come to a complete stop.

The car will have changed its speed by 120 km/h in those 20 seconds. First, convert the speed to International System units:

The acceleration will be:

Application of Graham's law: hydrogen diffusion rate (8308)

F_y_Q — 2024-09-12T04:06:10Z

Determine the diffusion rate of hydrogen, knowing that the diffusion rate of oxygen is 2 minutes.

Graham's law relates the diffusion rates of two gases to their molecular masses. If the gases are A and B, the relationship is:

For hydrogen and oxygen, both being diatomic, the molecular masses are:

The relationship between their diffusion rates will be:

This means hydrogen diffuses four times faster than oxygen, so the diffusion rate of hydrogen will be 0.5 minutes, or 30 seconds.

Principle of dimensional homogeneity (8304)

F_y_Q — 2024-09-11T10:46:47Z

What is the principle of dimensional homogeneity?

This principle states that equations relating physical quantities must be consistent, meaning that the same dimensions must appear on both sides of the equation. The best way to understand this is through an example.

The speed at which an object moves under the influence of acceleration is:

(Ec. 1)

Speed is the ratio of distance to the time taken to cover it. In terms of dimensions, it is expressed as:

Acceleration is the ratio of the change in speed to the time taken for that change, so it can be expressed as:

If you apply this to equation (Eq. 1), you will have:

As you can see, the dimensions are the same on both sides of the equation.