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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 488 psi and the lecture hall is 23°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.

Answer :

IthaloAbreu

Answer:

2.05 moles

Explanation:

Considering it as an ideal gas, we must use the ideal gas law:

PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.082 atm*L/mol*K), and T is the temperature.

If the gauge reads zero when 14.7 psi of gas remains, it means that the pressure must be equal to atmospheric pressure, so 1 atm = 14.7 psi.

P = 488 psi * 1atm/14.7psi = 33.20 atm

T = 23ºC + 273 = 296 K

33.20*1.50 = n*0.082*296

24.272n = 49.8

n = 2.05 moles

The number of moles of sulfur dioxide are in the bottle is 2.05 moles

Ideal gas law:

According to the above law

we know that

PV = nRT,

Here P is the pressure,

V is the volume, n is the number of moles,

R is the gas constant (0.082 atm*L/mol*K),

And T is the temperature.

Now

P = 488 psi * 1atm/14.7psi = 33.20 atm

T = 23ºC + 273 = 296 K

33.20*1.50 = n*0.082*296

24.272n = 49.8

So,

n = 2.05 moles

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