Question

A gas occupy 400ml volume at 47degree celcius and 800mm of Hg pressure. What will be its pressure at a height where the temperature is 27 degree celcius and volume of the gas is 450ml^2​

Answer 1

Explanation:

p1 = 800mm

p2=?

v1=400ml

v2=450ml

t1=273+47=320

t2=273+27=300

(P1V1) /T1 = (P2V2) /T2

(800×400)/320 = (P2×450)/300

P2 = (800×400)/320 × 300/450

P2 = 666.67mm Hg

Answer 2

Answer: Pressure at a height where temperature is $27$°C is $666.67 mm of Hg.$

Explanation:

Given: $P_{1} = 800 mm of Hg$, $T_{1} = 47$°C $= 47 + 273 = 320 K$, $V_{1}= 400 mL$,

$P_{2} = ?$, $T_{2} = 27$°C$= 27 + 273 = 300 K$ , $V_{2} = 450 mL$

Using ideal gas equation:

$PV = nRT$

$P =$ pressure of gas, $V =$ Volume occupied by gas, $n =$ no. of moles of gas, $R=$ gas constant and $T =$temperature of gas

As $R$ is a constant and $n$ is same; we can write the above equation as:

$\frac{PV}{T} = constant$

or $\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }$

To find $P_{2}$;

$\frac{800 mm * 400 mL }{320 K} = \frac{P_{2} * 450 mL}{300 K}$

$P_{2} = 666.67 mm of Hg$

Therefore pressure at a height where temperature is $27$°C is $666.67 mm of Hg.$

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