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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You're on a roll — Question 5: The average kinetic energy of a molecule of a gas depends on the absolute temperature of the gas. According to the kinetic theory of gases, the average translational kinetic energy of a gas molecule is directly proportional to the absolute temperature. The correct option is (b) Temperature. --- Question 6: Step 1: Identify the given values and convert temperatures to Kelvin. Initial volume V_1 = 370 L. Initial temperature T_1 = 16^ C = 16 + 273 = 289 K. Initial pressure P_1 = 150 Pa. Final temperature T_2 = -21^ C = -21 + 273 = 252 K. Final pressure P_2 = 420 Pa. We need to find the final volume V_2. Step 2: Apply the Combined Gas Law. The Combined Gas Law states (P_1V_1)/(T_1) = (P_2V_2)/(T_2). Rearrange the formula to solve for V_2: V_2 = (P_1V_1T_2)/(P_2T_1) Step 3: Substitute the values and calculate V_2. V_2 = (150 Pa)(370 L)(252 K)(420 Pa)(289 K) V_2 = (13986000)/(121380) L V_2 ≈ 115.225 L The volume of the hydrogen gas at -21^ C and 420 Pa is 115.23 L. --- Question 7: Step 1: Identify the given values and convert temperature and molar mass to SI units. Temperature T = 0^ C = 0 + 273 = 273 K. Boltzmann constant k = 1.38 × 10^-23 J/K. Avogadro's number N_A = 6.022 × 10^23 molecule/mol. Molar mass of nitrogen M = 28 g/mol = 0.028 kg/mol. Step 2: Calculate the Universal Gas Constant R. The Universal Gas Constant R can be calculated as R = k N_A. R = (1.38 × 10^-23 J/K) × (6.022 × 10^23 mol^-1) R ≈ 8.31036 J/(mol·K) Step 3: Calculate the root mean square speed (v_rms). The formula for the root mean square speed is v_rms = sqrt((3RT)/(M)). v_rms = sqrt(3 × (8.31036 J/(mol)·K)) × (273 K)0.028 kg/mol v_rms = sqrt((6806.98)/(0.028)) m/s v_rms = sqrt(243106.4) m/s v_rms ≈ 493.06 m/s The root mean square speed of a nitrogen molecule at 0^ C is 493.06 m/s. --- Question 8: Step 1: Identify the given values and convert them to SI units. Mass of nitrogen m = 2.0 g. Volume of tube V = 30 cm^3 = 30 × (10^-2 m)^3 = 30 × 10^-6 m^3. Temperature T = 20^ C = 20 + 273 = 293 K. Molar mass of nitrogen M = 28 g/mol = 0.028 kg/mol. Universal Gas Constant R = 8.314 J/(mol·K). Step 2: Calculate the number of moles (n) of nitrogen. n = (m)/(M) = 2.0 g28 g/mol n ≈ 0.071428 mol Step 3: Apply the Ideal Gas Law to find the pressure P. The Ideal Gas Law is PV = nRT. Rearrange to solve for P: P = (nRT)/(V) P = (0.071428 mol) × (8.314 J/(mol·K)) × (293 K)30 × 10^-6 m^3 P = (174.16)/(30 × 10^-6) Pa P = 5.805 × 10^6 Pa The nitrogen pressure in the tube when it is warmed to 20^ C is 5.81 × 10^6 Pa. Drop the next question.