Final answer:
The volume of a gas in a balloon under the given conditions of pressure (1.5 × 10^5 Nm^-2), temperature (18°C), and amount (0.5 moles) is approximately 9.6894 liters, calculated using the Ideal Gas Law.
Step-by-step explanation:
The question involves determining the volume of a gas contained in a balloon using the Ideal Gas Law. The provided information includes the pressure (1.5 × 10^5 Nm^-2), the temperature (18°C), and the amount of substance (0.5 moles), along with the universal gas constant (R=8.314 J/(mol·K)).
To find the volume, we first convert the temperature to Kelvin by adding 273.15. So, the temperature in Kelvin is 18 + 273.15 = 291.15 K. Then, we apply the Ideal Gas Law formula:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Solving for V gives us:
V = (nRT) / P
V = (0.5 moles × 8.314 J/(mol·K) × 291.15 K) / (1.5 × 10^5 Nm^-2)
V ≈ 0.0096894 m^3 or 9.6894 L
Therefore, the volume of the gas in the balloon is approximately 9.6894 liters.