This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
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Step 1: Identify the given values for Problem 1. We are given: Pressure (P) = 1.34 atm Temperature (T) = 303 K Density () = 1.77 g/L Gas constant (R) = 0.08206 L·atm/(mol·K) Step 2: Use the ideal gas law rearranged for molar mass. The ideal gas law is PV = nRT. We know that the number of moles n = (m)/(M), where m is mass and M is molar mass. Substituting n into the ideal gas law: PV = (m)/(M)RT. Rearranging for density ( = (m)/(V)): P = (m)/(V) (RT)/(M) P = (RT)/(M). Solving for molar mass (M): M = ( RT)/(P) Step 3: Substitute the values and calculate the molar mass. M = (1.77 g/L) × (0.08206 L · atm/(mol · K)) × (303 K)1.34 atm M = 44.0049666 g · atm/mol1.34 atm M = 32.8395273 g/mol Rounding to three significant figures: M = 32.8 g/mol The molar mass of the gas is 32.8 g/mol. Step 4: Identify the given values and convert units for Problem 2. We are given: Volume (V) = 7240 ft^3 Pressure (P) = 745 torr Temperature (T) = 21 °C Conversion: 1 ft^3 = 28.3 L Gas: Helium (He) Molar mass of Helium (M_He) = 4.00 g/mol Gas constant (R) = 0.08206 L·atm/(mol·K) Convert volume from ft^3 to L: V = 7240 ft^3 × 28.3 L1 ft^3 = 204772 L Convert pressure from torr to atm: P = 745 torr × 1 atm760 torr = 0.980263 atm Convert temperature from °C to K: T = 21^ + 273.15 = 294.15 K Step 5: Use the ideal gas law to find the number of moles (n). The ideal gas law is PV = nRT. Solving for n: n = (PV)/(RT) n = (0.980263 atm) × (204772 L)(0.08206 L · atm/(mol · K)) × (294.15 K) n = 200730.07 L · atm24.139 L · atm/mol n = 8315.6 mol Step 6: Convert moles of helium to grams of helium. Mass (m) = number of moles (n) × molar mass (M_He) m = 8315.6 mol × 4.00 g/mol m = 33262.4 g Rounding to three significant figures: m = 33300 g The mass of helium required is 33300 g.