Question

0.542 grams of an unknown gas is added to a 3.0 Liter vessel. The temperature is 28°C and the pressure is 16 psi. Which of the following could be the gas added to thevessel?N2HeH2O2ArO F2Kr

Answer 1

Answer: the unknown gas mentioned by the question is He

Step-by-step explanation:

The question requires us to identify the gas (choosing from a list given), considering the information provided.

The following data was provided by the question:

mass of gas = m = 0.542 g

volume of gas = V = 3.0 L

temperature = T = 28 °C

pressure of gas = P = 16 psi

To solve this problem, we'll need to go through the following steps:

1) Calculate the number of moles of gas considering the volume, temperature and pressure given (note that we'll need to convert the pressure and temperature to the appropriate units);

2) Calculate the molar mass of the unknown gas from the mass given by the question and the number of moles calculated;

3) Compare the molar mass obtained to the list of gases provided.

Next, we'll go through these steps to solve the problem:

1) We can apply the equation of ideal gases, shown below, to calculate the number of moles of gas using the information provided by the question:

`P* V=n* R* T`

where R is the constant of gases (0.08205 L.atm/K.mol.

Rearranging this equation to calculate n (number of moles), we'll have:

`n=(P* V)/(R* T)`

Note that, due to the units of R (L.atm/K.mol), we'll need to convert the temperature from °C to Kelvin and the pressure from psi to atm:

`\begin{gathered} T(K)=T(°C)+273.15 \\ T(K)=28°C+273.15=301.15K \end{gathered}`
`1atm=14.696psi\rightarrow P=16psi*(1psi)/(14.696atm)=1.09atm`

Therefore, the volume, temperature and pressure that will be applied to the equation of gases are, respectively, 3.0 L, 301.15K and 1.09 atm:

`n=(P* V)/(R* T)\rightarrow n=(1.09atm*3.0L)/(0.08205atm.L/K.mol*301.15K)=0.13mol`

Therefore, the amount of unknown gas in the container is 0.13 mol.

2) Next, we must use the mass given (0.542g) and number of moles calculated (0.13 mol) to obtain the molar mass of the gas.

Knowing that the number of moles of a substance can be obtained by dividing the mass of the sample by its molar mass, we can write:

`\begin{gathered} number\text{ of moles \lparen mol\rparen = }\frac{mass\text{ \lparen g\rparen}}{molar\text{ mass \lparen g/mol\rparen}}\rightarrow n=(m)/(M) \\ M=(m)/(n) \end{gathered}`

Thus, applying the values obtained so far:

`M=(m)/(n)=(0.542g)/(0.13mol)=4.1g/mol`

Therefore, the molar mass of the unknown gas is 4.1 g/mol.

3) At last, we must compare the molar mass obtained with the gases provided by the question. Among the gases given, only He presents molar mass close to the value obtained (molar mass of He gas = 4.00 g/mol).

Therefore, the unknown gas mentioned by the question is He.