What is the temperature of a gas with a molar mass of 2.0 g/mol that has a density of 2.00 g/L and a pressure of 44.8 atm, using the Ideal Gas Law?

• A. 100 K
• B. 273 K
• C. 150 K
• D. 546 K

Answer: (B)

Verified step by step guidance

1. Start by recalling the Ideal Gas Law, which is expressed as: $PV=nRT$, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
2. To find the temperature, rearrange the Ideal Gas Law to solve for T: $T=\frac{PV}{nR}$.
3. Since the density of the gas is given, use the relationship between density, molar mass, and volume: $d=\frac{m}{V}$, where d is density, m is mass, and V is volume. Rearrange to find V: $V=\frac{m}{d}$.
4. Substitute the given density (2.00 g/L) and molar mass (2.0 g/mol) into the equation to find the volume of 1 mole of gas: $V=\frac{2.0}{2.00}$ L.
5. Now, substitute the values for P (44.8 atm), V (calculated volume), n (1 mole), and R (0.0821 L·atm/mol·K) into the rearranged Ideal Gas Law to solve for T.