Answer :
To find out how many moles of gaseous nitrogen are contained in the bulb, we can use the Ideal Gas Law, which is a common equation in chemistry for gases. The Ideal Gas Law is represented as:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure of the gas in atmospheres (atm)
- [tex]\( V \)[/tex] is the volume of the gas in liters (L)
- [tex]\( n \)[/tex] is the number of moles of gas
- [tex]\( R \)[/tex] is the ideal gas constant, which is approximately [tex]\( 0.0821 \, \text{L} \cdot \text{atm}/(\text{mol} \cdot \text{K}) \)[/tex]
- [tex]\( T \)[/tex] is the temperature in Kelvin (K)
Given:
- The pressure ([tex]\( P \)[/tex]) is 1.79 atm
- The volume ([tex]\( V \)[/tex]) is 100.2 L
- The temperature ([tex]\( T \)[/tex]) is 563 K
We want to solve for the number of moles ([tex]\( n \)[/tex]). To do this, we rearrange the Ideal Gas Law equation to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{PV}{RT} \][/tex]
Now, plug in the known values:
- [tex]\( P = 1.79 \, \text{atm} \)[/tex]
- [tex]\( V = 100.2 \, \text{L} \)[/tex]
- [tex]\( R = 0.0821 \, \text{L} \cdot \text{atm}/(\text{mol} \cdot \text{K}) \)[/tex]
- [tex]\( T = 563 \, \text{K} \)[/tex]
Substituting these values into the equation gives:
[tex]\[ n = \frac{1.79 \times 100.2}{0.0821 \times 563} \][/tex]
When you perform this calculation, you find that the number of moles of gaseous nitrogen is approximately 3.88 moles.
This step-by-step method allows you to determine the number of moles of gas using the Ideal Gas Law.
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure of the gas in atmospheres (atm)
- [tex]\( V \)[/tex] is the volume of the gas in liters (L)
- [tex]\( n \)[/tex] is the number of moles of gas
- [tex]\( R \)[/tex] is the ideal gas constant, which is approximately [tex]\( 0.0821 \, \text{L} \cdot \text{atm}/(\text{mol} \cdot \text{K}) \)[/tex]
- [tex]\( T \)[/tex] is the temperature in Kelvin (K)
Given:
- The pressure ([tex]\( P \)[/tex]) is 1.79 atm
- The volume ([tex]\( V \)[/tex]) is 100.2 L
- The temperature ([tex]\( T \)[/tex]) is 563 K
We want to solve for the number of moles ([tex]\( n \)[/tex]). To do this, we rearrange the Ideal Gas Law equation to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{PV}{RT} \][/tex]
Now, plug in the known values:
- [tex]\( P = 1.79 \, \text{atm} \)[/tex]
- [tex]\( V = 100.2 \, \text{L} \)[/tex]
- [tex]\( R = 0.0821 \, \text{L} \cdot \text{atm}/(\text{mol} \cdot \text{K}) \)[/tex]
- [tex]\( T = 563 \, \text{K} \)[/tex]
Substituting these values into the equation gives:
[tex]\[ n = \frac{1.79 \times 100.2}{0.0821 \times 563} \][/tex]
When you perform this calculation, you find that the number of moles of gaseous nitrogen is approximately 3.88 moles.
This step-by-step method allows you to determine the number of moles of gas using the Ideal Gas Law.