Chapter 5: Problem 130
When a litre flask contains \(4 g\) of \(\mathrm{H}_{2}\) and \(14 \mathrm{~g}\) of \(\mathrm{N}_{2}\) at ordinary temperature the partial pressure is (1) \(6 / 7\) times of the total pressure (2) \(5 / 4\) times of the total pressure (3) \(4 / 5\) times of the total pressure (4) None
Short Answer
Expert verified
The partial pressure is \(\frac{4}{5}\) times the total pressure. Option (3) is correct.
Step by step solution
Over 22 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Number of Moles
The concept of moles is fundamental in chemistry. It allows us to count entities like atoms and molecules by weighing them. The mole is a unit that stands for a specific number of particles, usually atoms or molecules. One mole equals Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles.
To calculate the number of moles (n), use the formula:
\[ \text{Number of moles} (n) = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \] For instance, to find the number of moles of hydrogen gas (H\(_2\)), knowing it weighs 4 grams and its molar mass is 2 g/mol:
\[ n_{\text{H}_2} = \frac{4 \text{ g}}{2 \text{ g/mol}} = 2 \text{ moles of } H_2 \]
This basic calculation helps in understanding how many molecules are involved in a chemical reaction.
To calculate the number of moles (n), use the formula:
\[ \text{Number of moles} (n) = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \] For instance, to find the number of moles of hydrogen gas (H\(_2\)), knowing it weighs 4 grams and its molar mass is 2 g/mol:
\[ n_{\text{H}_2} = \frac{4 \text{ g}}{2 \text{ g/mol}} = 2 \text{ moles of } H_2 \]
This basic calculation helps in understanding how many molecules are involved in a chemical reaction.
Ideal Gas Law
The ideal gas law is a handy tool in chemistry to relate measurable properties of gases, including pressure, volume, temperature, and the number of moles. The law is represented by the equation:
\[ PV = nRT \]
Where:
This equation lets us calculate any one property if we have the other three. For example, if we know the pressure and volume of a gas, along with the number of moles and the temperature, we can calculate the universal gas constant. This law is especially useful in predicting the behavior of gases under different conditions.
\[ PV = nRT \]
Where:
- P is pressure
- V is volume
- n is the number of moles
- R is the universal gas constant (8.314 J/mol·K)
- T is temperature in Kelvin
This equation lets us calculate any one property if we have the other three. For example, if we know the pressure and volume of a gas, along with the number of moles and the temperature, we can calculate the universal gas constant. This law is especially useful in predicting the behavior of gases under different conditions.
Chemical Calculations
Chemical calculations often involve determining pressures, volumes, or moles of gases using given data.
In this exercise, we start with the number of moles of \(H_2\) and \(N_2\) gases in the flask:
\[ n_{\text{H}_2} = \frac{4 \text{ g}}{2 \text{g/mol}} = 2 \text{ moles of } H_2 \] \[ n_{\text{N}_2} = \frac{14 \text{ g}}{28 \text{ g/mol}} = 0.5 \text{ moles of } N_2 \]
Next, we find the total number of moles:
\[ n_{\text{total}} = n_{\text{H}_2} + n_{\text{N}_2} = 2 + 0.5 = 2.5 \text{ moles} \]
For partial pressures, use the formula based on the mole fraction and total pressure:
\[ P_{\text{H}_2} = \frac{n_{\text{H}_2}}{n_{\text{total}}} = \frac{2}{2.5} = 0.8 \]
\[ P_{\text{N}_2} = \frac{n_{\text{N}_2}}{n_{\text{total}}} = \frac{0.5}{2.5} = 0.2 \]
Finally, the total pressure is the sum of the partial pressures:
\[ P_{\text{total}} = P_{\text{H}_2} + P_{\text{N}_2} = 0.8 + 0.2 = 1 \] These detailed steps ensure accurate chemical calculations, enabling us to predict and understand the behavior of gases in different scenarios.
In this exercise, we start with the number of moles of \(H_2\) and \(N_2\) gases in the flask:
\[ n_{\text{H}_2} = \frac{4 \text{ g}}{2 \text{g/mol}} = 2 \text{ moles of } H_2 \] \[ n_{\text{N}_2} = \frac{14 \text{ g}}{28 \text{ g/mol}} = 0.5 \text{ moles of } N_2 \]
Next, we find the total number of moles:
\[ n_{\text{total}} = n_{\text{H}_2} + n_{\text{N}_2} = 2 + 0.5 = 2.5 \text{ moles} \]
For partial pressures, use the formula based on the mole fraction and total pressure:
\[ P_{\text{H}_2} = \frac{n_{\text{H}_2}}{n_{\text{total}}} = \frac{2}{2.5} = 0.8 \]
\[ P_{\text{N}_2} = \frac{n_{\text{N}_2}}{n_{\text{total}}} = \frac{0.5}{2.5} = 0.2 \]
Finally, the total pressure is the sum of the partial pressures:
\[ P_{\text{total}} = P_{\text{H}_2} + P_{\text{N}_2} = 0.8 + 0.2 = 1 \] These detailed steps ensure accurate chemical calculations, enabling us to predict and understand the behavior of gases in different scenarios.
