This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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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: P_1 V_1 = P_2 V_2 Where: P_1 is the initial pressure V_1 is the initial volume P_2 is the final pressure V_2 is the final volume Step 1: Identify the given values and make necessary assumptions. Initial pressure, P_1 = 740 torr Initial volume, V_1 = 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, P_2 = 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, V_2. Step 2: Rearrange Boyle's Law to solve for V_2. V_2 = (P_1 V_1)/(P_2) Step 3: Substitute the known values into the equation. V_2 = (740 torr) × (7.0 mL)760 torr Step 4: Calculate the final volume. V_2 = 5180 torr · mL760 torr V_2 ≈ 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. V_2 ≈ 6.8 mL The volume of the oxygen gas at standard pressure (760 torr) and constant temperature is approximately 6.8 mL.