Question

At STP,250cm³of gas had a mass of 0.36g.
1. What result does this give for the molar mass of gas​

Answer 1

As we know STP means Standard Temperature and Pressure. Where, Pressure is 1 atm and temperature is 273 K and also Ideal gas law ( PV=nRT) or (PV = w/M RT)

Where –

• P = Pressure in atm
• V = Volume in L
• n = moles
• R = Ideal gas law constant
• T = Temperature in K
• w = Given Mass
• M = Molar Mass

Now, according to the question –

• w = 0.36 g
• V = 250 cm³ or $\sf 250 \times 10^{-3}$ L
• P = 1 atm
• T = 273 K
• R = 0.0821 atm L/ mol K

Calculation –

$\qquad$ $\pink{\twoheadrightarrow\bf PV = nRT}$

$\qquad$ $\pink{\twoheadrightarrow\bf PV = \dfrac{w}{M}\times RT}$

$\qquad$ $\twoheadrightarrow\sf\dfrac{w}{M} = \dfrac{PV}{RT}$

$\qquad$ $\twoheadrightarrow\sf \dfrac{M}{w} = \dfrac{RT}{PV}$

$\qquad$ $\twoheadrightarrow\sf M = \dfrac{RT}{PV}\times w$

$\qquad$ $\twoheadrightarrow\sf M = \dfrac{0.0821 \times 273 }{1 \times 250\times 10^{-3} } \times 0.36$

$\qquad$ $\twoheadrightarrow\sf M = \dfrac{22.4}{250\times 10^{-3}} \times 0.36$

$\qquad$ $\twoheadrightarrow\sf M = 89.6\times 0.36$

$\qquad$ $\twoheadrightarrow\sf M = 32.275$

$\qquad$ $\pink{\twoheadrightarrow\bf M = 32.3\: g}$

• Henceforth, Molar Mass is 32.3 g

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Answer 2

The result obtained for the molar mass of the gas is 32.14 g/mol

How to determine the mole of the gas

From the question given above, the following data were obtained:

•Volume (V) = 250 cm³ = 250/1000 = 0.25 L

•Pressure (P) = STP = 1 atm

•Temperature (T) = STP = 273 K

•Gas constant (R) = 0.0821 atm.L/Kmol

•Number of mole (n) =?

The number of mole of the gas can be obtained by using the ideal gas equation as illustrated below:

PV = nRT

Divide both side by RT

n = PV / RT

n = (1 × 0.25) / (0.0821 × 273)

n = 0.0112 mole

How to determine the molar mass of the gas

The number of mole of the gas can be obtained as follow:

•Number of mole of gas = 0.0112 mole

•Mass of gas = 0.36 g

•Molar mass of gas =?

Molar mass = mass / mole

Molar mass of gas = 0.36 / 0.0112

Molar mass of gas = 32.14 g/mol

Learn more about ideal gas equation:

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