Answer:
number of moles = 0.08175 moles
Explanation:
To solve this question, we will use the ideal gas law:
PV = nRT
where:
P is the pressure = 1 atm
V is the volume of the gas = 2 liters
n is the number of moles we want to find
R is the general gas constant = 0.0821 L-atm/mol-K
T is the temperature = 25°C = 25 + 273 = 298°K
Now, substitute with the givens in the equation to get n as follows:
PV = nRT
1 * 2 = n * 0.0821* 298
n = [tex] \frac{1*2}{0.0821 * 298} = 0.08175 [/tex] moles
Hope this helps :)
[tex]\boxed{{\text{0}}{\text{.06 mol}}}[/tex] of nitrogen are contained in a 2 L cola bottle at atmospheric pressure and room temperature.
Further Explanation:
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 is as follows:
[tex]{\text{PV}} = {\text{nRT}}[/tex] ......(1)
Here, P is the pressure of nitrogen.
V is the volume of nitrogen.
T is the absolute temperature of nitrogen.
n is the number of moles of nitrogen.
R is the universal gas constant.
Rearrange equation (1) to calculate the number of moles of nitrogen.
[tex]{\text{n}} = \frac{{{\text{PV}}}}{{{\text{RT}}}}[/tex] ......(2)
Firstly, the temperature is to be converted into K. The conversion factor for this is,
[tex]{\text{0 }}^\circ {\text{C}} = {\text{273 K}}[/tex]
So the temperature of nitrogen is calculated as follows:
[tex]\begin{aligned}{\text{Temperature}}\left( {\text{K}}\right)&=\left( {25 + 273} \right)\;{\text{K}}\\&=298\;{\text{K}}\\\end{aligned}[/tex]
The pressure of nitrogen is 1 atm.
The volume of nitrogen is 2 L.
The temperature of nitrogen is 298 K.
Universal gas constant is 0.0821 L atm/K mol.
Substitute these values in equation (2).
[tex]\begin{aligned}{\text{n}}&=\frac{{\left({{\text{1 atm}}}\right)\left({{\text{2 L}}}\right)}}{{\left({{\text{0}}{\text{.0821 L atm/K mol}}}\right)\left({{\text{298 K}}} \right)}}\\&={\text{0}}{\text{.0817 mol}}\\&\approx {\text{0}}{\text{.08 mol}}\\\end{aligned}[/tex]
As we know, air contains 78 % of nitrogen. So the moles of nitrogen are calculated as follows:
[tex]\begin{aligned}{\text{Number of moles of }}{{\text{N}}_2} &=\left({{\text{0}}{\text{.08 mol}}}\right)\left({\frac{{{\text{78}}\;{\text{\% }}}}{{{\text{100}}\,{\text{\% }}}}}\right)\\&={\text{0}}{\text{.0624 mol}}\\&\approx {\mathbf{0}}{\mathbf{.06 mol}}\\\end{aligned}[/tex]
Learn more:
1. Which statement is true for Boyle’s law: https://brainly.com/question/1158880
2. Calculation of volume of gas: https://brainly.com/question/3636135
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Ideal gas equation
Keywords: ideal gas, pressure, volume, absolute temperature, equation of state, hypothetical, universal gas constant, moles of gas, initial, final, moles of nitrogen, 0.08 mol, 0.06 mol, 298 K, 273 K, P, V, n, R, T, room temperature, atmospheric pressure.
