What volume of hydrogen gas measured at 27celcius and 723 torr may be prepared by the reaction of 8.88 grams of gallium with an excess of hydrochloric acid?
Ga+ HCl ==> GaCl3 + H2
Balance the reaction...
2Ga + 6HCl yields 2GaCl3+2H2
so you get a mole of Hydrogen for each mole of Ga.
How many moles of Gallium is 8.88 grams?
Now, convert that number of moles to volume H2.
Volume= nRT/P
To determine the volume of hydrogen gas produced, we need to apply the ideal gas law. The ideal gas law states that:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
To find the volume of hydrogen gas, we need to calculate the number of moles of hydrogen gas produced.
Step 1: Calculate the number of moles of gallium (Ga) using its molar mass.
Molar mass of Ga = 69.72 g/mol
Number of moles of Ga = mass of Ga / molar mass of Ga
Number of moles of Ga = 8.88 g / 69.72 g/mol
Step 2: Calculate the number of moles of hydrogen gas produced based on the balanced chemical equation.
From the balanced equation: 2 moles of Ga produce 3 moles of H2.
So, our conversion factor is 3 moles H2 / 2 moles Ga.
Number of moles of H2 = (Number of moles of Ga) * (3 moles H2 / 2 moles Ga)
Step 3: Convert the temperature from Celsius to Kelvin.
T(K) = T(°C) + 273.15
T(K) = 27°C + 273.15
Step 4: Substitute the values into the ideal gas law equation.
PV = nRT
We will assume the pressure is given in torr, so we need to convert it to atm.
1 atm = 760 torr
So, the pressure is 723 torr / 760 torr/atm.
V = (nRT) / P
Substitute the values:
V = [(Number of moles of H2) * (0.0821 L·atm/(mol·K)) * (T(K))] / P
Calculate the volume using the given values, and plug them into the equation:
V = [(Number of moles of H2) * (0.0821 L·atm/(mol·K)) * (T(K))] / P
Note: At this point, you need to substitute the values for (Number of moles of H2), T(K), and P into the equation and calculate it.
To determine the volume of hydrogen gas produced, we need to use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure (in atm or torr)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K) or 62.36 L·torr/(mol·K))
T = temperature (in Kelvin)
First, we need to find the number of moles of hydrogen gas produced.
We can start by calculating the number of moles of gallium (Ga) using its molar mass.
The molar mass of Ga is 69.72 g/mol.
So, moles of Ga = mass of Ga / molar mass of Ga
moles of Ga = 8.88 grams / 69.72 g/mol
moles of Ga ≈ 0.1272 mol
According to the balanced equation, the stoichiometric ratio between Ga and H2 is 1:1. This means that 1 mole of Ga reacts to produce 1 mole of H2.
Therefore, the number of moles of H2 produced is also 0.1272 mol.
Now, we can use the ideal gas law to find the volume of H2 gas.
However, we need to convert the temperature from Celsius to Kelvin.
Kelvin = Celsius + 273.15
Temperature in Kelvin = 27°C + 273.15 = 300.15 K
Now we have all the values needed to calculate the volume of hydrogen gas.
PV = nRT
V = (nRT) / P
V = (0.1272 mol * 0.0821 L·atm/(mol·K) * 300.15 K) / 723 torr
Note: Convert torr to atm (divide by 760).
V ≈ (0.1272 mol * 0.0821 L·atm/(mol·K) * 300.15 K) / (723 torr / 760 torr/atm)
By simplifying the equation, we find:
V ≈ 0.0160 L
Therefore, the volume of hydrogen gas produced is approximately 0.0160 liters when measured at 27°C and 723 torr.