What is the density (in g/L) of hydrogen gas at 20.0 °C and a pressure of 1655 psi?

Video transcript

Hey everyone. And welcome back. What is the density in grams per liter of hydrogen gas at 20 °C and a pressure of 1655 9. There are four answer choices. A 9.43 B 2.02 C 10.6 ND 4.95. All of them are given in grams per liter. So now we can use the ideal gas law which states that PV equals NRC. And we can derive an equation in terms of density. Let's remember that N is the number of moles. We can use mass and divided by molar mass. That's the definition of moles. So if we plug this into our equation, we end up with PV equals M divided by capital M. So that's mass divided by molar mass multiplied by RT. If we multiply both sides by the molar mass, we get PV M equals M RT. And because we want to derive the formula in terms of density, let's recall that density is mass divided by a volume, meaning it would be sensible to divide both sides by volume such that we get M divided by VRT on the right hand side, which is essentially our density. Do we get an equation P capital M equals D RT? If we're looking for density, we can rearrange this formula for density and state that density equals PM divided by RT. Well done. So we can essentially substitute everything into this equation. First of all, we need to use pressure 1655 C. Apparently, we need to convert this into atmospheres. So we're going to use a conversion factor. One atmosphere is essentially equivalent to 14.79. This allows us to perform the conversion right now, we need to include the molar mass of hydrogen gas because it's diatomic, it's two, we're going to use 2.016 g per mole. And now let's think about our denominator, the universal gas constant, 0.08206 liters multiplied by atmospheres, divided by m multiplied by Kelvin. What about the temperature? Well, we need to use the absolute temperature. We take 20 °C at 273.15 Calvin and we get 293.15 Kelvin. So now if we calculate the result, we get 9.4 we grams per liter. And that would be our final answer. If we take a look at the answer, choices, we can conclude that the correct answer is option a 9.43 g per liter is the density of hydrogen gas at the given temperature and pressure. Thank you for watching.