Question

unit 2 worksheet 3 - pvtn problems
on each of the problems below, start with the given p, v, t, or n; then make a decision as to
how a change in p, v, t, or n will affect the starting quantity. multiply the initial value of the
quantity of interest by the appropriate ratio for each known variable pair. draw particle
diagrams of the initial and final conditions.

1. what would be the new pressure if 250 cm³ of gas at standard pressure is compressed

to a volume of 150 cm³? (n and t = constant)

1. the pressure in a bicycle tire is 105 psi at 25°c in santa rosa. you take the bicycle up to

tahoe, where the temperature is - 5°c. what is the pressure in the tire?
(v and n = constant)

1. a sample of gas occupies 150 ml at 25°c. what is its volume when the temperature is

increased to 50°c? (p and n = constant)

Explanation:

Step1: Convert temperatures to Kelvin

For problem 2:
Initial temperature \(T_1 = 25^{\circ}C+273 = 298K\)
Final temperature \(T_2=- 5^{\circ}C + 273=268K\)
For problem 3:
Initial temperature \(T_1 = 25^{\circ}C+273 = 298K\)
Final temperature \(T_2=50^{\circ}C + 273=323K\)

Step2: Apply gas laws

Problem 1:

Since \(n\) and \(T\) are constant, use Boyle's law \(P_1V_1 = P_2V_2\).
Given \(P_1 = 1\space atm\), \(V_1=250\space cm^3\), \(V_2 = 150\space cm^3\)
\(P_2=\frac{P_1V_1}{V_2}=\frac{1\times250}{150}=\frac{5}{3}\approx1.67\space atm\)

Problem 2:

Since \(V\) and \(n\) are constant, use Gay - Lussac's law \(\frac{P_1}{T_1}=\frac{P_2}{T_2}\)
\(P_2=\frac{P_1T_2}{T_1}=\frac{105\times268}{298}\approx94.3\space psi\)

Problem 3:

Since \(P\) and \(n\) are constant, use Charles's law \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\)
\(V_2=\frac{V_1T_2}{T_1}=\frac{150\times323}{298}\approx162.5\space mL\)

Answer:

1. The new pressure is approximately \(1.67\space atm\)
2. The pressure in the tire is approximately \(94.3\space psi\)
3. The volume of the gas is approximately \(162.5\space mL\)