Question

What pressure in kPa is exerted by 94.60 g CO2 at 57.00 ℃ in 0.7500 L?

Answer 1

7859.98 KPa

Step-by-step explanation:

Step 1:

Data obtained from the question. This includes the following:

Mass of CO2 = 94.60g

Temperature (T) = 57℃

Volume (V) = 0.75 L

Pressure (P) =?

Step 2:

Determination of the number of mole of CO2.

Mass of CO2 = 94.60g

Molar Mass of CO2 = 12 + (2x16) = 12 + 32 = 44g/mol

Number of mole of CO2 =?

Number of mole = Mass/Molar Mass

Number of mole of CO2 = 94.60/44

Number of mole of CO2 = 2.15 moles

Step 3:

Conversion of celsius temperature to Kelvin temperature.

Temperature (Kelvin) = temperature (celsius) + 273

Temperature = 57℃ + 273 = 330K

Step 4:

Determination of the pressure. This is illustrated below:

The pressure can be obtained by using the ideal gas equation as shown below:

PV = nRT

Temperature (T) = 330K

Volume (V) = 0.75 L

Number of mole (n) = 2.15 moles

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

Pressure (P) =?

PV = nRT

0.75 x P = 2.15 x 0.082 x 330

Divide both side by 0.75

P = (2.15 x 0.082 x 330)/0.75

P = 77.572 atm

Step 5:

Conversion of the pressure in atm to KPa. This is illustrated below:

1 atm = 101.325 KPa

Therefore, 77.572 atm = 77.572x101.325 = 7859.98 KPa

Answer 2

The correct answer is 8,026 x 10³ kPa

Step-by-step explanation:

We have gaseous CO₂ at the following conditions:

mass = 94.60 g

T= 57.00ºC = 330 K

V= 0.7500 L

We can use the ideal gas equation to calculate the pressure (P):

P x V = n x R x T

⇒ P = (n x R x T)/V

We need n, which is the number of moles of the gas. In order to calculate this, we have to calculate first the molecular weight (MM) of CO₂ as follows:

MM(CO₂)= Molar mass C + (2 x Molar mass O) = 12 g/mol + (2 x 16 g/mol) = 44 g/mol

Now, we can calculate the number of moles (n) of CO₂ from the mass and the molecular weight as follows:

n = Mass/MM = 96.60 g/44 g/mol = 2.19 moles

Now we have all the data. So, we introduce the data in the previos equation and calculate the pressure P:

P = (n x R x T)/V = (2.19 mol x 0.082 L.atm/K.mol x 330 K)/0.7500 L = 79.0152 atm

Finally, we have to convert the pressure from atm to kPa. For this, we know that 1 atm = 1,01325 x 10⁵ Pa and 1 kPa= 1000 Pa.

79.0152 atm x 1,01325 x 10⁵ Pa/atm x 1 kPa/1000 Pa = 8,026 x 10³ kPa