Question

What pressure (in atm) will a sample of o2 gas occupy at 100.0 ml, if o2 has a volume of 25.00 ml at 2.0 atm?

Answer 1

Assuming that the O2 gas acts like an ideal gas, we find the following expression to be approximates of the behaviour of this gas:

P V = n R T                   ---> 1

where,

P = pressure exerted by the gas

V = volume occupied

n = number of moles

R = universal gas constant

T = absolute temperature

Further, we assume that the number of moles and the temperature are constant, hence reducing equation 1 into the form:

P V = k                         ---> 2

where k is a constant. Therefore we can equate two states:

P1 V1 = P2 V2

Since P1, V1 and V2 are given and we are to look for P2:

25 mL * 2 atm = 100 mL * P2

P2 = 0.5 atm

Answer 2

The sample of ${{\text{O}}_2}$ gas at volume 100 mL will occupy a pressure of  

$\boxed{{\text{0}}{\text{.5 atm}}}$

Further explanation:

Ideal gas:

An ideal gas contains a large number of randomly moving particles that are supposed to have perfectly elastic collisions among themselves. It is just a theoretical concept, and practically no such gas exists. But gases tend to behave almost ideally at a higher temperature and lower pressure.

Ideal gas law is considered as the equation of state for any hypothetical gas. The expression for the ideal gas equation of gas is as follows:

${\text{PV}}={\text{nRT}}$                …… (1)                                                                         

Here,

P is the pressure of the gas.

V is the volume of gas.

n denotes the number of moles of gas.

R is the gas constant.

T is the temperature of gas.

Boyle’s law:

It is an experimental gas law that describes the relationship between pressure and volume of the gas. According to Boyle's law, the volume of the gas is inversely proportional to the pressure of the system, provided that the temperature and the number of moles of gas remain constant.

If the temperature and number of moles of gas are constant then the equation (1) will become as follows:

${\text{PV}}={\text{constant}}$                  …… (2)                                                                                                        

Or it can also be expressed as follows:

${{\text{P}}_1}{{\text{V}}_1}={{\text{P}}_2}{{\text{V}}_2}$                        …… (3)                                                                                        

Here,

${{\text{P}}_1}$ is the initial pressure.

${{\text{P}}_2}$ is the final pressure.

${{\text{V}}_1}$ is the initial volume.

${{\text{V}}_2}$ is the final volume.

Rearrange the equation (3) for ${{\text{P}}_2}$  , and we get,

${{\text{P}}_2}=\frac{{{{\text{P}}_1}{{\text{V}}_1}}}{{{{\text{V}}_2}}}$                      …… (4)                                                                                 

${{\text{P}}_1}$ is 2.0 atm.

${{\text{V}}_1}$ is 25 mL.

${{\text{V}}_2}$ is 100 mL.

Substitute the values of ${{\text{P}}_1}$ , ${{\text{V}}_1}$ and ${{\text{V}}_2}$  in equation(4).

$\begin{aligned}{{\text{P}}_2}&=\frac{{\left( {{\text{25 atm}}}\right)\times\left({{\text{2 mL}}}\right)}}{{\left({{\text{100 mL}}}\right)}}\\&={\text{0}}{\text{.5 atm}}\\\end{aligned}$

Learn more:

1. How many atoms of hydrogen are present in 2.92g of a water molecule: brainly.com/question/899408

2. Identify the intermolecular forces present between given molecules: brainly.com/question/10107765

Answer details:

Grade: Senior school

Subject: Chemistry

Chapter: Ideal gas equation.

Keywords: ideal gas, pressure, volume, temperature, number of moles, initial, final, equation, 25 atm, 2 mL, 100 mL, and 0.5 atm.