Question

A container, with a fixed volume, filled with a fixed amount of an ideal gas has an original pressure of 2.00 atm at 30.0◦c. what is the pressure if the temperature is increased to 50.0◦c. express your answer in atmospheres.

Answer 1

Since the volume doesn't change, and we assume that that
no heat is allowed to escape from the container, the pressure
of the gas will be directly proportional to its absolute temperature. 

Absolute temperature = Celsius temperature + 273 K.

at 50°C, the absolute temperature is  323 K .

at 30°C, the absolute temperature is  303 K.

So, as the gas is warmed, the pressure will rise to  (323/303)
of where it started.

(323/303) x (2.00 atm)  =  (1.066) x (2.00 atm)  =  2.132 atm
 

Answer 2

The pressure is about 2.13 atm

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Further explanation

The Ideal Gas Law that needs to be recalled is:

$\large {\boxed {PV = nRT} }$

P = Pressure (Pa)

V = Volume (m³)

n = number of moles (moles)

R = Gas Constant (8.314 J/mol K)

T = Absolute Temperature (K)

Let us now tackle the problem !

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Given:

initial pressure = P₁ = 2.00 atm

initial temperature = T₁ = 30 + 273 = 303 K

final temperature = T₂ = 50 + 273 = 323 K

Unknown:

final pressure = P₂ = ?

Solution:

We will use ideal gas law as follows:

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

$\frac{P_1V}{T_1} = \frac{P_2V}{T_2}$

$\frac{P_1}{T_1} = \frac{P_2}{T_2}$

$\frac{2.00}{303} = \frac{P_2}{323}$

$P_2 = \frac{323}{303} \times 2.00$

$P_2 \approx 2.13 \texttt{ atm}$

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Learn more

• Minimum Coefficient of Static Friction : brainly.com/question/5884009
• The Pressure In A Sealed Plastic Container : brainly.com/question/10209135
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454

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Answer details

Grade: High School

Subject: Physics

Chapter: Pressure

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Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant , Liquid , Pressure, Ideal , Gas , Volume , Temperature