Question

A 1.10 −g sample of dry ice is added to a 765 −mL flask containing nitrogen gas at a temperature of 25.0 ∘C and a pressure of 715 mmHg . The dry ice is allowed to sublime (convert from solid to gas) and the mixture is allowed to return to 25.0 ∘C.

What is the total pressure in the flask?

Express your answer using three significant figures.

Answer 1

Step 1: Explanation

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions.

We know the ideal gas equation, PV = nRT

where, R=universal gas constant ( it may vary in unit like 0.08206 L-atm mol-1 K-1)

T=Temperature ( Unit = Kelvin )

P=Pressure ( Unit= atm )

V=Volume ( Unit=Litre )

n=moles ( Unit = mol )

Step 2: calculate the moles of dry ice (CO2)

Molar mass of dry ice (CO2) = 44.01 g/mol

mass given = 1.10 g

Moles of dry ice = mass / molar mass = 1.10 g /44.01 g/mol = 0.02499432 mol

Step 3: Calculate the pressure of dry ice

moles(n) = 0.02499432 mol

volume(V) = 765 mL= 0.765 L

[ Note : => 765 mL × (1 L / 1000 mL ) = 0.765 L ]

Temperature = (25 +273.15)K = 298.15 K

By using the ideal gas equation

P = nRT / V

P = (0.02499432 molx 0.08206 L -atm /K -mol) x 298.15 K) / ( 0.765 L) = 0.799367 atm = 607.519 mmHg

[ Note: 1 atm = 760 mmHg => 0.799367 atm × (760 mmHg / 1 atm ) = 607.519 mmHg

Step 4: Calculation of total pressure

Given,

pressure of nitrogen gas = 715 mmHg

we got pressure of dry ice = 607 mmHg

Total pressure of flask = pressure of dry ice + pressure of nitrogen gas

=> Total pressure of flask = 607 mmHg + 715 mmHg = 1322 mmHg

hence, the total pressure of the flask = 1.32 × 103 mmHg