A gas sample collected in a laboratory syringe occupies a volume of 600\text{ cm}^3 at 27^… — JAMB UTME

A gas sample collected in a laboratory syringe occupies a volume of $600\text{ cm}^3$ at $27^\circ\text{C}$ and $1.0\text{ atm}$ pressure. What is the volume of the gas when the pressure is increased to $2.0\text{ atm}$ and the temperature is raised to $81^\circ\text{C}$ ?

$354\text{ cm}^3$ Cevap
B
$900\text{ cm}^3$
C
$708\text{ cm}^3$
D
$1416\text{ cm}^3$

Cevap

The final volume of the gas is

354\text{ cm}^3

Using the General Gas Law

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

with absolute temperatures

T_1 = 300\text{ K}

(

27^\circ\text{C}

) and

T_2 = 354\text{ K}

(

81^\circ\text{C}

), the calculation yields

V_2 = \frac{1.0 \times 600 \times 354}{2.0 \times 300} = 354\text{ cm}^3

Adım Adım Çözüm

Convert temperatures from Celsius to Kelvin

T_1 = 27 + 273 = 300\text{ K}

and

T_2 = 81 + 273 = 354\text{ K}

Gas laws require absolute temperature values on the Kelvin scale.

Set up the General Gas Law equation

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \implies V_2 = \frac{P_1 V_1 T_2}{P_2 T_1}

Pressure, volume, and temperature all change simultaneously for a fixed mass of gas.

Substitute the known values and calculate

V_2

V_2 = \frac{1.0\text{ atm} \times 600\text{ cm}^3 \times 354\text{ K}}{2.0\text{ atm} \times 300\text{ K}} = 354\text{ cm}^3

Simplifying

\frac{600}{2.0 \times 300} = 1

leaves

1 \times 354 = 354\text{ cm}^3

Anahtar Kavram

General Gas Law (Combined Gas Law)

Tahmini Süre:1m 15s

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