A sample of sulfur dioxide occupies a volume of 652 mL at 40.° C and

720 mm Hg. What volume will the sulfur dioxide occupy at STP?

Considering the ideal gas law and the definiton of STP, the volume of sulfur dioxide is 537.6 mL.

So, in first place you have to know that, an ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T).

The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of the gases:

P×V = n×R×T

In this case you know that a sample of sulfur dioxide occupies a volume of 652 mL (equal to 0.652 L, being 1000 mL=1 L) at 40° C (equal to 313 K, being 0 C= 273 K) and  720 mm Hg (equal to 0.947369 atm, being 760 mmHg= 1 atm).

Then, replacing the values in the ideal gas law:

0.947369 atm× 0.652 L= n× 0.082 × 313 K

Solving:

n=0.024 moles

On the other side, the STP conditions refer to the standard temperature and pressure. Pressure values at 1 atmosphere and temperature at 0 ° C are used and are reference values for gases. And in these conditions 1 mole of any gas occupies an approximate volume of 22.4 liters.

Then you can apply the following rule of three: if by definition of STP conditions, 1 mole of the gas occupies 22.4 L, 0.024 moles occupies how much volume?

volume= 0.5375 L= 537.6 mL

Finally, the volume of sulfur dioxide is 537.6 mL.

Learn more:

The volume of sulfur dioxide at STP is 538 mL

Explanation:

Step 1: Data given

Volume = 652 mL = 0.652 L

Temperature = 40.0 °C = 313 K

The pressure is 720 mmHg = 720 / 760 atm = 0.947369 atm

Step 2: Calculate the number of moles sulfur dioxide

p*V = n*R * T

⇒with p = the pressure of the gas = 0.947369 atm

⇒with V = the volume of the gas = 0.652 L

⇒with n = the number of moles of gas = TO BE DETERMINED

⇒with R = the gas constant = 0.08206 L*atm/mol*K

⇒with T = the temperature = 313 K

n = (p*V) / (R*T)

n = ( 0.947369 atm  * 0.652 L) / (0.08206 L*atm/mol*K * 313 K)

n = 0.0240 moles

Step 3: Calculate volume  sulfur dioxide occupy at STP

STP = 1 atm and 273 K

1 mol has a volume of 22.4 L

0.0240 moles have a volume of 22.4 L * 0.0240 = 0.538 L = 538 mL

The volume of sulfur dioxide at STP is 538 mL

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