Question

Synthesis Questions Use available resources to help you answer the following questions. 1. Consider the Erlenmeyer flask with the stopper tightly inserted. How do you think the pressure would change if you doubled the number of molecules (moles) in the flask? Explain your prediction! 2. Based on your answer to the previous question, what kind of mathematical relationship is there between the pressure and number of moles nof a gas? What is the mathematical representation of that relationship? 3. Combine the relationship between pressure and the number of moles of the gas with the relationship you obtained for pressure, temperature, and volume. 4. Direct proportionality can be turned into an equation by using a constant. For example, if A B , then with a constant, for example, k, the relationship turns into a mathematical equation: A = kB. Using the constant R, turn the proportionality relationship between P. n. T. and V into an equation! 5. The equation you just derived is referred to as the "Ideal Gas Law which relates pressure, temperature, number of moles, and volume for gases. The constant R is referred to as the universal gas constant and has the value of 8.314 (L kPa)/(mol K). Arrange the ideal Gas Law so you have P and V on the left and the other terms on the right. This is a more common form of this law.

Answer 1

1. Considering that the Erlenmeyer flask is tightly covered with the stopper such that no molecules inside can go outside and vice-versa and also considering the gas to be ideal, doubling the number of molecules(or moles) within the  flask will double the pressure inside the flask. This is because increasing the number of moles increases the number of times each second a particle strikes the wall. Hence, the pressure increases.

2. Based on the above statement, it is clearly understood that the pressure inside the Erlenmeyer flask is directly proportional to the number of moles within the flask. Thus, mathematically, it can be written as:

Pan

(or,  )

P = constant xn

where P is the pressure, n is the no. of moles, and a constant of proportionality.

3. Relationship between pressure, temperature and volume derivation:

According to BOYLE'S LAW,

V  $\propto$$\frac{1}{P}$

where, V is the volume and P is pressure.

According to CHARLE'S LAW,

V7

Comparing both the proportionality equations, we have

VOX

Now combining it with the equation ,  

Pan

we have.

Von

4. The proportionality equation can be written as

V =R x n7

5. The ideal gas equation is as follows:

PV = nRT