The pressure of an ideal gas is 782mmHg at 35°C in a box with a volume of 2,239mL. What is the number of moles? If this gas is oxygen, O2, what is the number of molecules present?

1. 0.091 mole

2. 5.48x10^22 molecules

Explanation:

Data obtained from the question include:

P (pressure) = 782mmHg

We need to convert 782mmHg to atm. This is illustrated below

760mmHg = 1atm

782mmHg = 782/760 = 1.03atm

T (temperature) = 35°C = 35 + 273 = 308K

V (volume) = 2239mL

We need to convert 2239mL to L. This is illustrated below:

1000mL = 1L

2239mL = 2239/1000 = 2.239L

n (number of mole) =?

R (gas constant) = 0.082atm.L/Kmol

1. Using the ideal gas equation PV = nRT, the number of mole 'n' can obtain as shown below:

PV = nRT

n = PV /RT

n = (1.03x2.239)/(0.082x308)

n = 0.091 mole

Therefore, the number of mole of the gas is 0.091 mole

2. The second part of the question suggest that the ideal gas is oxygen (O2).

Now, we can find the the number of molecules present in 0.091 mole of O2 as follow:

From Avogadro's hypothesis, 1 mole of any substance contains 6.02x10^23 molecules. This means that 1 mole of O2 also contains 6.02x10^23 molecules.

Now, if 1 mole of O2 contains 6.02x10^23 molecules,

Therefore 0.091 mole of O2 will contain = 0.091 x 6.02x10^23 = 5.48x10^22 molecules

There are 5.49*10^22 molecules O2

Explanation:

Step 1: Data given

The pressure = 782 mm Hg = 782 /760 atm = 1.03026 atm

Temperature = 35 °C = 308 K

Volume = 2239 mL 2.239 L

Step 2: Calculate moles of gas

p*V = n*R*T

⇒with p = the pressure of the gas = 1.03026 atm

⇒with V = the volume of the gas = 2.239 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 = 35 °C = 308 K

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

n = (1.03026 * 2.239) / (0.08206*308)

n = 0.091268 moles of gas

Step 3: Calculate molecules O2

Number of molecules = moles * number of Avogadro

Number of molecules = 0.091268 moles * 6.02 * 10^23

Number of molecules = 5.49*10^22 molecules O2

There are 5.49*10^22 molecules O2