Question

If the volume of a given mass of gas at 300 k and a pressure of 880mmHg is 3.5 dm3, what is the volume of the gas at s.t.p? (Standard pressure= 760mmHg and Standard temperature= 273k)

Answer 1

The volume of gas at s.t.p is 3.7 liters.

Given:

The volume of a given mass of gas at 300 k and pressure of 880mmHg is 3.5 dm3 (Standard pressure= 760mmHg and Standard temperature= 273k).

To Find:

The volume of gas at s.t.p.

Solution:

To find the volume of gas at s.t.p we will follow the following steps:

According to the ideal gas equation:

$pv = nrt$

Here, n is the number of moles, p is the pressure in the mm of Hg and v is the volume in liters.

t is the temperature in Kelvin.

r is the universal gas constant.

Now,

As pressure and volume is directly proportional to temperature so,

We can write a relation like:

$\frac{p1v1}{t1} = \frac{p2v2}{t2} (s.t.p)$

According to the question:

In the first case:

Pressure (p1) = 880 mm Hg

Volume(v1) = 3.5 dm³ or 3.5 liters

T1 = 300K

In the second case at s.t.p:

Pressure (p2) = 760 mm Hg

Volume (v2) = To be determined

T2 = 273K

Now,

Putting values in the above equation we get,

$\frac{880 \times 3.5}{300} = \frac{760 \times v2}{273} (s.t.p)$

Now,

$v2 = \frac{880 \times 3.5 \times 273}{300 \times 760} = \frac{8.8 \times 3.5 \times 273}{3 \times 760} = 3.69 \:or \:3.7\: liters$

Henceforth, the volume of gas at s.t.p is 3.7 liters.

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