Calculate the density of nitrogen gas (in g/L) at 923 mm Hg and 31.6 °C.

How do we calculate the density of nitrogen gas at 923 mm Hg and 31.6 °C?

What is the ideal gas law equation we can use?

How do we convert the given pressure and temperature to suitable units?

Calculation of Nitrogen Gas Density

To calculate the density of nitrogen gas at 923 mm Hg and 31.6 °C, we need to utilize the ideal gas law equation.

First, we convert the given pressure from mm Hg to atm and the temperature from Celsius to Kelvin.

Next, we solve for moles of nitrogen gas using the rearranged ideal gas law equation.

Then, we find the molar mass of nitrogen gas and substitute the values to calculate the moles (n).

Lastly, we determine the density of nitrogen gas by using the mass-moles relationship and find it to be approximately 1.334 g/L.

Explanation of Nitrogen Gas Density Calculation

When trying to determine the density of nitrogen gas at a specific pressure and temperature, we turn to the ideal gas law equation: PV = nRT. In this case, we are given the pressure as 923 mm Hg and the temperature as 31.6 °C.

First, we convert the pressure from mm Hg to atm by using the conversion factor 1 atm = 760 mm Hg. This gives us a pressure of approximately 1.2158 atm.

Next, we convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius value. This results in a temperature of approximately 304.75 K.

With the pressure and temperature converted to suitable units, we rearrange the ideal gas law equation to solve for moles of nitrogen gas (n). This involves using the ideal gas constant (R) and the volume (V).

After finding the moles of nitrogen gas, we then need to determine the molar mass of nitrogen gas, which is around 28.02 g/mol. Substituting the values into the equation allows us to calculate the moles (n) to be approximately 0.0476 V.

Finally, using the formula for density (mass/volume), we can find the density of nitrogen gas at the given conditions. By substituting the moles (n) and molar mass into the equation, we arrive at a density of approximately 1.334 g/L.

This process involves converting units, utilizing the ideal gas law, and understanding the relationship between mass, moles, and volume to determine the density of nitrogen gas accurately.