Use R = 8.2 *10^-5 m³ . atm/mol .K and N_A = 6.02 * 10²³ mol^-1.The approximate number of air molecules in a 1 m³ volume at room temperature (300 K)and atmospheric pressure is: A)41 B)450 C)2.4 *10²⁵ D)2.7*10²⁶ E)5.4 * 10²⁶

Question

Quizplus · Accepted Answer

Using the ideal gas law, we can calculate the number of air molecules in a 1 m³ volume:
n = (P V) / (R T)
n = (1 atm * 1 m³) / (8.2 J/(mol K) * 300 K)

Convert pressure and volume to SI units:
n = (101325 Pa * 1 m³) / (8.2 J/(mol K) * 300 K)

Convert from Pa to atm and simplify:
n = (101325 Pa / 1013250 Pa/atm * 1 atm * 1 m³) / (8.2 J/(mol K) * 300 K)
n = 1.23 * 10²⁵ / (8.2 J/(mol K) * 300 K)

Substitute the given values and simplify:
n = 1.23 * 10²⁵ / (8.2 * 300 * 10⁻³ * 6.02 * 10²³)
n ≈ 2.4 * 10²⁵

Therefore, the closest choice is C, 2.4 x 10^25.

Use R = 82 *10-5 M3

Use R = 82 *10^-5 M³