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Helium Was Required to Fill the Balloon? Find the Molar Mass of 6.24 G of an Unknown Gas That Occupies 2.5 Lat 18.3^circ C and 100.5

Question

helium was required to fill the balloon? Find the molar mass of 6.24 g of an unknown gas that occupies 2.5 Lat 18.3^circ C and 100.5 kPa.

Solution

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Answer

Here's how to solve this problem using the Ideal Gas Law:**1. Convert units to standard SI units:*** **Temperature:** Convert Celsius to Kelvin: 18.3°C + 273.15 = 291.45 K* **Pressure:** Convert kPa to Pa: 100.5 kPa * 1000 Pa/kPa = 100500 Pa* **Volume:** 2.5 L is already in a suitable unit (we'll convert to m³ later as needed).**2. Use the Ideal Gas Law:**The Ideal Gas Law is PV = nRT, where:* P = pressure (Pa)* V = volume (m³)* n = number of moles* R = ideal gas constant (8.314 J/(mol·K))* T = temperature (K)**3. Rearrange the Ideal Gas Law to solve for 'n' (number of moles):**n = PV / RT**4. Convert volume from Liters to cubic meters:**2.5 L * (1 m³/1000 L) = 0.0025 m³**5. Plug in the values and solve for 'n':**n = (100500 Pa * 0.0025 m³) / (8.314 J/(mol·K) * 291.45 K) n ≈ 0.104 moles**6. Calculate the molar mass:**Molar mass (M) = mass (m) / number of moles (n)M = 6.24 g / 0.104 molesM ≈ 60 g/mol**Answer:** The molar mass of the unknown gas is approximately 60 g/mol.