Question

A given mass of a gas occupies 143 cm3 at 27°C and
700 mm Hg pressure. What will be its volume at 300 K
and 280 mm Hg pressure ?
[Ans. 357.5 cm]

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Answer 1

answer is 357.5cm^3

HOPE IT HELPS

Answer 2

Given

A given mass of a gas occupies 143 cm³ at 27°C and  700 mm Hg pressure

To Find

What will be its volume at 300 K  and 280 mm Hg pressure

Solution

We know that

Combined Gas Law

The ratio of the product of pressure, volume and temperature of a system remains constant

Mathematically

$\red{\rm \longrightarrow \dfrac{PV}{T}=k}$

Hence

$\pink{\rm \longrightarrow \dfrac{P_{1}V_{1}}{T_{1}}=\dfrac{P_{2}V_{2}}{T_{2}}}$

Here

• P = Pressure
• V = Volume
• T = Temperature

Units

• P = millimetres of mercury (mm Hg)
• V = cubic centimetre (cm³)
• T = Kelvin (K)

According to the question

We are asked to find its volume at 300 K  and 280 mm Hg pressure

Hence

We must find $\green{\rm "V_{2}"}$

Therefore

$\purple{\rm \longrightarrow V_{2}=\dfrac{P_{1}V_{1}T_{2}}{P_{2}T_{1}}}$

Given that

A given mass of a gas occupies 143 cm³ at 27°C and  700 mm Hg pressure. What will be its volume at 300 K  and 280 mm Hg pressure

Hence

• P₁ = 700 mm Hg
• V₁ = 143 cm³
• T₁ = 27°C = 27 + 273 K = 300 K
• P₂ = 280 mm Hg
• T₂ = 300 K

Substituting the values

We get

$\blue{\rm \longrightarrow V_{2}=\dfrac{700 \times 143 \times 300}{280 \times 300} \ cm^{3}}$

Cancelling out similar terms

We get

$\green{\rm \longrightarrow V_{2}=\dfrac{700 \times 143}{280} \ cm^{3}}$

On further simplification

We get

$\orange{\rm \longrightarrow V_{2}=\dfrac{100100}{280} \ cm^{3}}$

Therefore

$\red{\rm \longrightarrow V_{2}=357.5 \ cm^{3}}$

Hence

Its volume at 300 K  and 280 mm Hg pressure will be 375.5 cm³