A gaseous product of a reaction is collected at 280K and 0.95 atm. Given R=0.0821L⋅atmmol⋅K

, what is the molar mass of the gas, in grams per mole, if 5.49 g of gas occupies 4.92 L?(1 point)
Responses

0.04 g/mol
0.04 g/mol

24 g/mol
24 g/mol

133 g/mol
133 g/mol

27 g/mol

1 answer

To determine the molar mass of the gas, we can use the Ideal Gas Law, which is given by the equation:

\[ PV = nRT \]

Where:

  • \( P \) = pressure (in atm)
  • \( V \) = volume (in liters)
  • \( n \) = number of moles of the gas
  • \( R \) = ideal gas constant (0.0821 L·atm/(mol·K))
  • \( T \) = temperature (in Kelvin)

We can rearrange the equation to solve for \( n \):

\[ n = \frac{PV}{RT} \]

Given:

  • \( P = 0.95 \) atm
  • \( V = 4.92 \) L
  • \( R = 0.0821 \) L·atm/(mol·K)
  • \( T = 280 \) K

Substituting the values into the equation:

\[ n = \frac{(0.95 , \text{atm}) \times (4.92 , \text{L})}{(0.0821 , \text{L·atm/(mol·K)}) \times (280 , \text{K})} \]

Calculating the denominator:

\[ 0.0821 \times 280 = 22.996 \]

Now calculate \( n \):

\[ n = \frac{(0.95) \times (4.92)}{22.996} \approx \frac{4.674}{22.996} \approx 0.203 \]

Now that we have the number of moles \( n \), we can calculate the molar mass \( M \) using the following formula:

\[ M = \frac{m}{n} \]

Where \( m \) is the mass of the gas (5.49 g).

Calculating the molar mass:

\[ M = \frac{5.49 , \text{g}}{0.203 , \text{mol}} \approx 27.0 , \text{g/mol} \]

Thus, the molar mass of the gas is approximately 27 g/mol.

The correct response is:

27 g/mol