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Correct Answer: 27
to solve the problem of identifying the molecular mass (m) of a gas under given conditions, we can employ the ideal gas law, which is represented by the equation pv = nrt. here, p represents the pressure of the gas, v is the volume, n is the number of moles of the gas, r is the ideal gas constant, and t is the temperature in kelvin.
given in the problem are the following values: p = 1 atm, v = 8.2 liters, t = 300 k, and the mass of the gas = 9 grams. the ideal gas constant (r) is typically 0.0821 l·atm/mol·k when pressure is in atmospheres, volume in liters, and temperature in kelvin.
the ideal gas law equation can be rearranged to solve for the number of moles (n) as n = pv/rt. substituting the given values into this equation:
\[ n = \frac{(1 \text{ atm}) \times (8.2 \text{ l})}{(0.0821 \text{ l·atm/mol·k}) \times (300 \text{ k})} \]
\[ n \approx \frac{8.2}{24.63} \approx 0.333 \text{ moles} \]
to find the molecular mass (m) of the gas, we use the relationship between the mass of the gas, its molecular mass, and the number of moles: mass = n × m. rearranging this to solve for m gives m = mass / n. substituting the known values:
\[ m = \frac{9 \text{ grams}}{0.333 \text{ moles}} \approx 27 \text{ g/mol} \]
therefore, the molecular mass of the gas is approximately 27 g/mol. this calculation assumes that the behavior of the gas is ideal, which is a reasonable approximation under many conditions but might vary slightly with different gases or under extreme conditions.
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