Considering the ideal gas law and the definition of Avogadro's Number, the correct option is option a. The temperature of a sample of CH₄ gas (10.34 g) in a 50.0 L vessel at 1.33 atm is 984 °C.
In first place, you have to know that ideal gases are a simplification of real gases that is done to study them more easily.
It is considered to be formed by point particles, do not interact with each other and move randomly. It is also considered that the molecules of an ideal gas, in themselves, do not occupy any volume.
An ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T).
The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of the gases:
P×V = n×R×T
In this case, being the molar mass of CH₄ being 16 [tex]\frac{g}{mole}[/tex], that is, the mass present in one mole of an element or compound, the number of moles that 10.34 grams contains is calculated as:
[tex]10.34 g*\frac{1 mole}{16.04 g} = 0.645 moles[/tex]
So, you know:
- P= 1.33 atm
- V= 50 L
- n= 0.645 moles
- R=0.082 (atm×L)/ (mol×K)
- T= ?
Replacing:
1.33 atm × 50 L= 0.645 moles× 0.082 (atm×L)/ (mol×K) ×T
Solving:
T= [1.33 atm × 50 L] ÷ [0.645 moles× 0.082 (atm×L)/ (mol×K) ]
T≅ 1257 K
Being 273 K equivalent to 0 C, then:
T= 1257 K= 984 C
In summary, the correct option is option a. The temperature of a sample of CH₄ gas (10.34 g) in a 50.0 L vessel at 1.33 atm is 984 °C.
Learn more about the ideal gas law: brainly.com/question/4147359?referrer=searchResults
