Question

Oxygen gas having a volume of 1000 cm³ at 40.0 C and 1.01x10⁵ Pa expands until its volume is 1500 Cm³ and its pressure is 1.06x10⁵ Pa. Find (a) the number of moles of oxygen present and b) the final temperature of the sample.

Answer 1

To find the number of moles of oxygen, we can use the ideal gas law equation PV = nRT. Rearranging the equation, we find that n = PV / RT. Plugging in the given values, we find that there are 3.66 moles of oxygen present. To find the final temperature of the sample, we can use the combined gas law equation P₁V₁ / T₁ = P₂V₂ / T₂. Solving for T₂, we find that the final temperature is 322.84 K.

Step-by-step explanation:

To find the number of moles of oxygen present, we can use the ideal gas law equation:

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.

Rearranging the equation to solve for n:

n = PV / RT

Plugging in the given values:

n = (1.01x10^5 Pa * 1000 cm³) / (8.314 J/(mol·K) * (40.0 + 273.15) K) = 3.66 moles

To find the final temperature of the sample, we can use the combined gas law equation:

P₁V₁ / T₁ = P₂V₂ / T₂

Plugging in the given values:

1.01x10^5 Pa * 1000 cm³ / (40.0 + 273.15) K = 1.06x10^5 Pa * 1500 cm³ / T₂

Solving for T₂:

T₂ = (1.06x10^5 Pa * 1500 cm³ * (40.0 + 273.15) K) / (1.01x10^5 Pa * 1000 cm³)

T₂ = 322.84 K