Calculate to three significant digits the density of sulfur hexafluoride gas at exactly 35 °C and exactly 1 atm. You can assume sulfur hexafluoride gas behaves as an ideal gas under these conditions.

Answer

📘 Problem Statement

Calculate the density of sulfur hexafluoride (SF₆) gas at 35 °C and 1.00 atm. Assume that SF₆ behaves as an ideal gas. Report your answer to three significant digits.

📐 Relevant Concepts

The ideal gas law is expressed as:

PV = nRT

We rearrange it using:
n = m / M and ρ = m / V

Combining these gives the density form of the ideal gas law:

ρ = (PM) / (RT)

🧮 Step-by-Step Calculation

Step 1: Convert Temperature to Kelvin

T = 35°C + 273.15 = 308.15 K

Step 2: Determine the Molar Mass of SF₆

Sulfur (S): 32.06 g/mol
Fluorine (F): 6 × 19.00 = 114.00 g/mol
Total molar mass: 146.06 g/mol

Step 3: Apply the Density Formula

ρ = (PM) / (RT)

P = 1.00 atm
M = 146.06 g/mol
R = 0.0821 L·atm/mol·K
T = 308.15 K

ρ = (1.00 × 146.06) / (0.0821 × 308.15) = 146.06 / 25.281415 ≈ 5.778 g/L

Step 4: Round to Three Significant Digits

✅ Final Answer

🔍 Summary

This calculation uses the density form of the ideal gas law. After converting temperature to Kelvin and calculating the molar mass of SF₆, the values are substituted into the formula and solved for density. The final result is reported to three significant digits.