If the volume of a given mass of gas at 298 K and pressure of 205.2 x 10\(^3\) Nm\(^{-2}\) is 2.12dm\(^3\), what is volume of the gas at s.t.p? (Standard pressure = 101.3 x 10\(^3\) Nm\(^{-2}\), Standard temperature = 273K)

39.3dm ³

22.4dm³

4.93dm³

3.93dm³

0.393dm³

Correct answer is D

V\(_1\) = 2.12dm\(^3\), V\(_2\) = ?

P\(_1\) = 205.2 x 10\(^3\) Nm\(^{-2}\), P\(_2\) = 101.3 x 10\(^3\) Nm\(^{-2}\)

T\(_1\) = 293K, T\(_2\) = 273K

Using \(\frac{P_1 * V_1}{T_1}\) = \(\frac{P_2 * V_2}{T_2}\)

: V\(_2\) = \(\frac{P_1 * V_1 * T_2}{P_2 * T_1}\)

→ \(\frac{205.2 x 10^3 * 2.12 * 273}{101.3 x 10^3 * 293}\)

= 4.0dm\(^3\)

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