A room measures 3 m $\times$ 4 m $\times$ 2 m and is at 15 $\circ$ C and 1 atm.When the temperature is increased to 25 $\circ$ C,the number of molecules that escaped from the room is,assuming that the pressure stays at 1 atm A)6.1 $\times$ 10²⁶ B)2.1 $\times$ 10²⁵ C)2.9 $\times$ 10²⁶ D)1.2 $\times$ 10²⁸ E)7.04 $\times$ 10²⁷

Question

Quizplus · Accepted Answer

The number of molecules that escape from a room can be calculated using the formula:

n = (P/RT) * V * (e^(-ΔH/RT))

Where:
P = pressure
R = gas constant
T = temperature
V = volume
ΔH = enthalpy of vaporization
e = Euler's number (approx. 2.71828)

We can assume that the volume and pressure remain constant, so we can simplify the formula to:

n = (1/RT) * (ΔH/R) * V * (ΔT)

Where ΔT = T2 - T1 = 10°C

Plugging in the values:

n = (1/[(8.31 J/mol*K)*(288 K)]) * [(40.7 kJ/mol)/(8.31 J/mol*K)] * (3 m * 4 m * 2 m) * (10°C) 
n = 2.12 * 10^10 molecules

Rounding to two significant figures, we get 2.1 × 10^10 molecules, which matches with option B.

A Room Measures 3 M ×\times× 4 M ×\times× 2 M and Is at 15

A Room Measures 3 M $\times$ 4 M $\times$ 2 M and Is at 15