Answer :
The ideal gas law relates to the pressure, volume, and temperature of the gas. The volume of the gas bubble at 99.3 kPa is 73.47 mL.
What is Boyle's law?
The inverse relationship between the pressure and the volume of the gas at constant temperature is given by Boyle's law. The formula for the Boyle's law is given as:
[tex]\rm P_{1}V_{1} = P_{2}V_{2}[/tex]
Given,
Initial pressure = 1.60 atm
Initial volume =45.0 mL
Final pressure = 0.98 atm (1 atm = 101.325 kPa)
The final volume is calculated as:
1.60 * 45 = 0.98 * V
V = 73.47 mL
Therefore, the volume of the gas bubble is 73.47 mL.
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Final answer:
The bubble of methane gas extracted from an underground natural gas reserve will occupy a volume of approximately 73.85 mL on the surface, assuming no change in temperature or amount of gas.
Explanation:
The question you asked is regarding gas laws, specifically Boyle's Law which states that the volume of a gas is inversely proportional to its pressure if the temperature and amount of gas remain constant. That is, P1 V1 = P2 V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In your case, we are given that a bubble of methane gas (CH4) has a volume of 45.0 mL at 1.60 atm. We're asked to find the volume of the gas when it reaches the surface where the atmospheric pressure is 99.3 kPa.
The key here is realizing that the pressures must be in the same units to use Boyle's Law. 1 atm is approximately 101.3 kPa, so 1.60 atm is about 162.08 kPa. Using Boyle's Law equation then, (162.08 kPa * 45.0 mL) / 99.3 kPa gives us a final volume of about 73.85 mL (rounded to 2 decimal places since we're given 3 significant figures). Therefore, the bubble will occupy a volume of 73.85 mL on the surface.
Learn more about Boyle's Law here:
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