To solve this, we use the Ideal Gas Law equation:
$PV = nRT$

Where:

• $P$ = Pressure (1.5 atm)
• $V$ = Volume (24.6 L)
• $n$ = Number of moles (what we’re solving for)
• $R$ = Ideal Gas Constant (0.0821 L·atm/mol·K)
• $T$ = Temperature (115.9 K)

Rearranging the equation for $n$:
$n = \frac{PV}{RT}$

Substituting the given values:

$n = \frac{(1.5)(24.6)}{(0.0821)(115.9)}$

Step-by-step calculation:

1. Calculate the numerator:
   $1.5 \times 24.6 = 36.9$

2. Calculate the denominator:
   $0.0821 \times 115.9 = 9.51439$

3. Divide the results:
   $n = \frac{36.9}{9.51439} \approx 3.88 \, \text{moles}$

Final Answer:

$n \approx 3.88 \, \text{moles}$

Would you like more details or have any questions?

Related Questions:

1. How does changing the temperature affect the number of moles if all else remains constant?
2. What happens if the pressure is halved while keeping the volume and temperature constant?
3. How would the result differ if the gas constant was given in $J/mol·K$?
4. What are the assumptions of the Ideal Gas Law?
5. Can the Ideal Gas Law be applied at very high pressures? Why or why not?

Tip:

Always check that the units in the Ideal Gas Law are consistent to avoid calculation errors.