Question

At 30 ∘C, how many oxygen molecules cross the lens in 1 hour?

a) 1.5 × 10^23
b) 2.5 × 10^23
c) 3.0 × 10^23
d) 3.5 × 10^23

Answer 1

At 30 °C, the number of oxygen molecules that cross the lens in 1 hour can be calculated using the ideal gas law. The closest answer is option b) 2.5 x 10^23.

Step-by-step explanation:

To determine the number of oxygen molecules that cross the lens in 1 hour at 30 °C, we can use the ideal gas law. The ideal gas law equation is:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Rearranging the equation to solve for n:

n = (PV) / (RT)

Given that we are looking for the number of oxygen molecules, we need to convert the volume to liters and the pressure to atmospheres:

V = 1 L

P = 1 atm

R = 0.0821 L · atm / (mol · K)

T = 30 °C + 273 = 303 K

Substituting these values into the equation:

n = (1 atm * 1 L) / (0.0821 L · atm / (mol · K) * 303 K) = 0.0409 mol

Finally, we can convert the moles to molecules using Avogadro's number:

n = 0.0409 mol * 6.022 x 10^23 molecules/mol = 2.464 x 10^22 molecules

Therefore, option b) 2.5 x 10^23 is the closest answer.