In preparation for a demonstration, your professor brings a 1.50-L bottle of sulfur dioxide into the lecture hall before class to allow the gas to reach room temperature. If the pressure gauge reads 988 psi and the lecture hall is 25°C, how many moles of sulfur dioxide are in the bottle? In order to solve this problem, you will first need to calculate the pressure of the gas. Hint: The gauge reads zero when 14.7 psi of gas remains.

4.81 moles

Explanation:

The total pressure of the gas = Pressure at which gauge reads zero + pressure read by it.

Pressure at which gauge reads zero = 14.7 psi

Pressure read by the gauge = 988 psi

Total pressure = 14.7 + 988 psi = 1002.7 psi

Also, P (psi) = P (atm) / 14.696

Pressure = 1002.7 / 14.696 = 68.2297 atm

Temperature = 25 °C

The conversion of T (°C) to T (K) is shown below:

T (K) = T (°C) + 273.15

So,

T = (25 + 273.15) K = 298.15 K

Volume = 1.50 L

Using ideal gas equation as:

PV=nRT

where,

P is the pressure

V is the volume

n is the number of moles

T is the temperature

R is Gas constant having value = 0.0821 L. atm/K. mol

Applying the equation as:

68.2297 atm * 1.5 L = n * 0.0821 L. atm/K. mol * 298.15 K

⇒n = 4.81 moles