What pressure will 2.6 × 10²³ molecules of H₂ exert in a 3.9 L container at 45 °C? A) 5.7 bar B) 1.7 bar C) 2.9 bar D) 3.4 bar E) 4.6 bar

Question

Quizplus · Accepted Answer

We can use the ideal gas law to solve for the pressure:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the number of molecules to moles:
n = N/N_A
where N is the number of molecules and N_A is Avogadro's number.

n = (2.6 × 10^21)/6.022 × 10^23 = 0.00432 mol

Next, we need to convert the temperature to Kelvin:
T = 45°C + 273.15 = 318.15 K

Now we can plug in the values and solve for P:
P = (nRT)/V
P = (0.00432 mol × 0.0821 L·atm/mol·K × 318.15 K) / 3.9 L
P = 2.885 atm

Finally, we convert from atm to bar:
1 atm = 1.01325 bar
P = 2.885 atm × 1.01325 bar/atm ≈ 2.92 bar

The closest answer choice is C, 2.9 bar.

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