Respuesta :
Answer: the pressure of the gas under the conditions given is 20.7kPa
Explanation:
The question requires us to determine the pressure of a gas, in kPa, knowing that there are 0.416 moles of this gas occupy 45.6 L of volume at standard temperature.
We can apply the rearranged equation for ideal gases to solve this problem, as shown below:
[tex]P\times V=n\times R\times T\rightarrow P=\frac{n\times R\times T}{V}[/tex]where P is the pressure of the gas, V is its volume (45.6 L), n is the number of moles of gas (0.416 mol), T is the temperature (standard temperature) and R is the constant of gases (we'll apply the value 8.314 kPa.L/mol.K).
The standard temperature can be defined as 273.15 K (or 0°C), as stated by the Standard Temperature and Pressure conditions (STP).
Applying the values provided by the question, we'll have:
[tex]\begin{gathered} \begin{equation*} P=\frac{n\times R\times T}{V} \end{equation*} \\ \\ P=(0.416\text{ mol\rparen}\times(8.314\text{ kPa.L/mol.K\rparen}\times(273.15\text{ K\rparen}\times\frac{1}{(45.6\text{ L\rparen}} \\ \\ P=3.46\text{ \lparen kPa.L/K\rparen}\times(273.15\text{ K\rparen}\times\frac{1}{(45.6\text{ }L)} \\ \\ P=(944.72\text{ kPa.L\rparen}\times\frac{1}{(45.6\text{L})} \\ \\ P=20.7\text{ kPa} \end{gathered}[/tex]Therefore, the pressure of the gas under the conditions given is 20.7kPa.
