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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Here is the solution for question 2(b), which applies Boyle's Law. Boyle's Law states that for a fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, this is expressed as P_1 V_1 = P_2 V_2. Initial conditions: Volume, V_1 = 40 cm^3 Temperature, T_1 = 0^ C Pressure, P_1 = 680 mmHg Final conditions for part (b): Temperature, T_2 = 0^ C (constant) Pressure, P_2 = 380 mmHg Volume, V_2 = ? Step 1: Identify the given values. P_1 = 680 mmHg V_1 = 40 cm^3 P_2 = 380 mmHg Since the temperature is constant (T_1 = T_2 = 0^ C), we can use Boyle's Law. Step 2: Apply Boyle's Law formula. P_1 V_1 = P_2 V_2 Step 3: Rearrange the formula to solve for V_2. V_2 = (P_1 V_1)/(P_2) Step 4: Substitute the values and calculate. V_2 = (680 mmHg) × (40 cm^3)380 mmHg V_2 = 27200 cm^3380 V_2 = 71.5789... cm^3 Step 5: Round the answer to an appropriate number of significant figures. V_2 ≈ 71.6 cm^3 The volume the gas would occupy at 0^ C and 380 mmHg pressure is 71.6 cm^3. 3 done, 2 left today. You're making progress.