Question

a 4.00 l sample of a gas is at a pressure of 2.00 atm. if the temperature remains constant, what will be its volume at 0.500 atm of pressure?
1.00 l
16.0 l
0.250 l
4.00 l
question 5
8 pts
a sample of gas has a volume of 200. ml at 20.0°c. what will be its volume at 40.0°c, pressure remaining constant?
18.8 ml
214 ml

1. ml
2. ml

Explanation:

Step1: Apply Boyle's Law for the first question

Boyle's Law is \(P_1V_1 = P_2V_2\). Given \(P_1 = 2.00\ atm\), \(V_1=4.00\ L\), \(P_2 = 0.500\ atm\). We need to find \(V_2\). Rearranging the formula gives \(V_2=\frac{P_1V_1}{P_2}\).
Substitute the values: \(V_2=\frac{2.00\ atm\times4.00\ L}{0.500\ atm}\)

$$V_2=\frac{8.00}{0.500}= 16.0\ L$$

Step2: Apply Charles's Law for the second question

Charles's Law is \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\). First, convert temperatures to Kelvin. \(T_1=(20.0 + 273.15)\ K=293.15\ K\), \(T_2=(40.0+ 273.15)\ K = 313.15\ K\), \(V_1 = 200\ mL\). Rearranging for \(V_2\) gives \(V_2=\frac{V_1T_2}{T_1}\)
Substitute the values: \(V_2=\frac{200\ mL\times313.15\ K}{293.15\ K}\)

$$V_2=\frac{62630}{293.15}\approx214\ mL$$

Answer:

For the first question: \(16.0\ L\)
For the second question: \(214\ mL\)