How many molecules of N₂ are in a 400.0 mL container at 780 mm Hg and 135°C? A)7)01 × 10^{21 molecules} B)7)38 × 10^{21 molecules} C)2)12 × 10^{22 molecules} D)2)23 × 10^{22 molecules}

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. We can rearrange this equation to solve for n: n = (PV)/(RT) Plugging in the given values: P = 780 mm Hg = 780/760 atm (converting to atm) V = 400.0 mL = 0.4 L (converting to L) T = 135°C = 408 K (converting to Kelvin) R = 0.0821 L atm/(mol K) (gas constant) We also need to know the molecular weight of N₂, which is (14 x 2) + (32 x 4) + (12 x 4) + (16 x 5) = 408 g/mol. Now we can calculate n: n = ((780/760) x 0.4) / (0.0821 x 408) n = 0.015 mol Finally, we can convert moles to molecules by multiplying by Avogadro's number (6.022 x 10^23 molecules/mol): 0.015 mol x 6.022 x 10^23 molecules/mol = 7.1385 x 10^21 molecules This is closest to answer choice B: 7.38 x 10^21 molecules.

How Many Molecules of N2 Are in a 400

How Many Molecules of N₂ Are in a 400