This problem involves a gas undergoing a change in pressure while its temperature remains constant. This scenario is described by Boyle's Law, which states that for a fixed mass of gas at constant temperature, the pressure (P) and volume (V) are inversely proportional. Mathematically, this is expressed as:
P1V1=P2V2
Where:
- P1 is the initial pressure
- V1 is the initial volume
- P2 is the final pressure
- V2 is the final volume
Step 1: Identify the given values and make necessary assumptions.
- Initial pressure, P1=740 torr
- Initial volume, V1=7.0 mL (Assuming "7.0 millimetres" is a typo for "7.0 milliliters", as millimeters is a unit of length, not volume, in this context.)
- Final pressure, P2=760 torr (Standard pressure is commonly taken as 1 atmosphere, which is equal to 760 torr.)
- Temperature remains constant.
- We need to find the final volume, V2.
Step 2: Rearrange Boyle's Law to solve for V2.
V2=P2P1V1
Step 3: Substitute the known values into the equation.
V2=760torr(740torr)×(7.0mL)
Step 4: Calculate the final volume.
V2=760torr5180torr⋅mL
V2≈6.815789 mL
Step 5: Round the answer to an appropriate number of significant figures. Since the initial volume (7.0 mL) has two significant figures, we round our answer to two significant figures.
V2≈6.8 mL
The volume of the oxygen gas at standard pressure (760 torr) and constant temperature is approximately 6.8mL.