In a specific region of interstellar space the atomic composition of gaseous matter is 89.1% atomic hydrogen and 10.9% helium, the temperature is 27K and the pressure is 2.58x10^-15Pa. What is the density of matter in this region? What is the particle density?

To find the density of matter in the given region, we first need to calculate the total number of particles (atoms) per unit volume, which is known as the particle density.

To calculate the particle density, we need to use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature.

Since we are given the pressure, we can rearrange the ideal gas law to solve for the number of moles (n):
n = PV / RT

Now, let's calculate the number of moles of the atomic hydrogen. The atomic composition of gaseous matter is given as 89.1% atomic hydrogen, so we assume that 89.1% of the total gas consists of atomic hydrogen.

To calculate the number of moles of atomic hydrogen:
n_hydrogen = (89.1 / 100) * n

Similarly, for helium:
n_helium = (10.9 / 100) * n

Now, the density of matter is given by the mass of matter divided by the volume it occupies. To calculate the density, we need to know the molar mass of atomic hydrogen and helium. The molar mass of hydrogen is approximately 1 gram/mole, and the molar mass of helium is approximately 4 grams/mole.

Let's assume a volume of 1 cubic meter for simplicity. You can adjust the volume according to your specific situation.

To calculate the density of matter:
Density_matter = (n_hydrogen * M_hydrogen + n_helium * M_helium) / V

where M_hydrogen is the molar mass of hydrogen, M_helium is the molar mass of helium, and V is the volume.

Now, let's plug in the values and calculate the density.

Given:
Atomic hydrogen composition: 89.1%
Helium composition: 10.9%
Temperature (T): 27 K
Pressure (P): 2.58 x 10^-15 Pa
Molar mass of hydrogen (M_hydrogen): 1 g/mol
Molar mass of helium (M_helium): 4 g/mol
Volume (V): 1 m^3

First, calculate the number of moles of gas (n) using the ideal gas law:
n = PV / RT

n = (2.58 x 10^-15 Pa) * (1 m^3) / (8.314 J/(mol·K) * 27 K) [Note: R = 8.314 J/(mol·K) is the universal gas constant]

Now, calculate the number of moles of atomic hydrogen (n_hydrogen) and helium (n_helium):
n_hydrogen = (89.1 / 100) * n
n_helium = (10.9 / 100) * n

Next, calculate the density of matter:
Density_matter = (n_hydrogen * M_hydrogen + n_helium * M_helium) / V

Substituting the values, we can calculate the density of matter.