If the molar mass of monatomic deuterium (D) is 2.0141 g, then what is the density of diatomic deuterium (D2) gas at 25.0°C and 1.00 atm?
I know the equation for density is: d=m/v
What equation(s) do I need to use to solve this?
Well, to find the density of diatomic deuterium gas, you need to use the ideal gas law equation, PV = nRT. In this equation, P represents the pressure, V represents the volume, n represents the number of moles, R is the ideal gas constant, and T represents the temperature.
Since we are given the pressure (1.00 atm) and the temperature (25.0°C), we can use these values in the equation. However, we still need to find the number of moles (n) and the volume (V) to calculate the density (d).
To find the number of moles (n), we can use the molar mass of diatomic deuterium (D2), which is twice the molar mass of monatomic deuterium (D). Since the molar mass of monatomic deuterium is given as 2.0141 g, the molar mass of diatomic deuterium would be 2 times that, which is 4.0282 g.
Now, to find the volume (V), we need to rearrange the ideal gas law equation in terms of volume: V = (nRT) / P.
So, the equation we'll use is V = (nRT) / P.
To use this equation, we'll need to know the value of the ideal gas constant, R, which is 0.0821 atm·L/mol·K.
Now, with all the information we have, we can calculate the density using the equation, d = m/V.
I hope this helps! Just remember, even science can't escape the clutches of equations.
To solve this problem, you will need to use the ideal gas law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
To find the molar mass of diatomic deuterium (D2), you simply add up the molar mass of two deuterium atoms (2.0141 g/mol + 2.0141 g/mol = 4.0282 g/mol).
First, you need to convert the given temperature in Celsius to Kelvin:
T(K) = T(°C) + 273.15
25.0°C + 273.15 = 298.15 K
Next, rearrange the ideal gas law equation to solve for moles:
n = PV / RT
Since the volume is not given, we can assume it is 1 mole of gas, so V = 1.00 mol.
Substituting the values into the equation, we get:
n = (1.00 atm) / (0.0821 L·atm/(mol·K) * 298.15 K)
Simplifying the equation, we get:
n ≈ 0.0402 moles
Now, we can calculate the mass of the diatomic deuterium gas by multiplying the number of moles by the molar mass:
mass = n * molar mass = 0.0402 mol * 4.0282 g/mol
mass ≈ 0.162 g
Finally, substitute the mass and volume into the density equation, d = m / V:
density = 0.162 g / 1.00 L
density ≈ 0.162 g/L
Therefore, the density of diatomic deuterium (D2) gas at 25.0°C and 1.00 atm is approximately 0.162 g/L.
To solve for the density of diatomic deuterium gas (D2) at 25.0°C and 1.00 atm using the equation d = m/v, you need to use the ideal gas law equation.
The ideal gas law equation is:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, convert the given temperature (25.0°C) to Kelvin by adding 273.15:
T = 25.0 + 273.15 = 298.15 K
To find the number of moles of diatomic deuterium gas (D2), you need to use the molar mass of monatomic deuterium (D) given that it is 2.0141 g.
Since diatomic deuterium gas (D2) consists of two deuterium atoms, the molar mass of D2 would be twice that of D.
Molar mass of D2 = 2 x Molar mass of D = 2 x 2.0141 g/mol = 4.0282 g/mol
Now, we can calculate the number of moles (n) using the formula:
n = molar mass (g) / molar mass (g/mol)
Let's assume you have a volume of 1.00 L of diatomic deuterium gas (D2).
Now, rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substitute the given values into the equation:
P = 1.00 atm
V = 1.00 L
R = 0.0821 L·atm/(mol·K)
T = 298.15 K
n = (1.00 atm) x (1.00 L) / (0.0821 L·atm/(mol·K)) x (298.15 K)
Calculate the value of n.
Once you have the number of moles (n), you can substitute it back into the density equation:
d = m/v
Where:
m = n x molar mass (g)
v = volume (L)
Substitute the values into the equation:
d = (n x molar mass) / v
Calculate the density by substituting the calculated values of n and the molar mass of D2, along with the given volume of 1.00 L.
Finally, calculate the density of diatomic deuterium (D2) gas at the given conditions.