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 173 psi and the lecture hall is 20°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.

0.66 mol

Explanation:

Zero Gauge pressure = 14.7 psi

Pressure read = 173 psi

Actual pressure = 173 psi - 14.7 psi = 158.3 psi

P (psi) = 1/14.696  P(atm)

So, Pressure = 10.77 atm

Given that:

Temperature = 20 °C

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

T(K) = T( °C) + 273.15  

So,  

T₁ = (20+ 273.15) K = 298.15 K

V = 1.50 L

Using ideal gas equation as:

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:

10.77 atm × 1.50 L = n ×0.0821 L atm/ K mol  × 298.15 K

⇒n = 0.66 mol

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