Question

In an underground gas reserve, a bubble of methane gas (C H4) has a volume of 45.0 m L at 1.60 atm pressure.part A: What volume, in milliliters, will the bubble occupy when it reaches the surface where the atmospheric pressure is 744 m m H g, if there is no change in the temperature and amount of gas?part B: What is the new pressure, in atmospheres, when the volume of the methane gas bubble expands to 125 m L, if there is no change in the temperature and amount of gas?

Answer 1

Answer:

$0.58\text{ atm}$

Explanation:

Here, we want to getthe new pressure

From Boyles' law, we know that the volume of a given mass of gas is inversely proprttional to the pressure at a constant temperature

Mathematically:

$P_1V_1\text{ = P}_2V_2$

where:

P1 is the initial pressure hich is 1.6 atm

P2 is the final pressure which is 744 mmHg (converting to atm by dividing by 760 mmHg, we have the aluea as 744/760 = 0.98 atm

V1 is 45 ml

V2 is ?

$V_2\text{ = }\frac{1.6\times45}{0.98}\text{ = 73.5 mL}$

Now, the gas expanded from 73. mL to 125 mL

The initial pressure woud now be 0.98 atm

Thus, we have the new pressure as:

$\begin{gathered} P_2\text{ = }\frac{73.5\times0.98}{125} \\ \\ P_2\text{ = 0.58 atm} \end{gathered}$