5.15g sample of gas containing only carbon and hydrogen has a volume of 785ml with a pressure of 1522 torr at a temperature of 280C. It is combusted in pure dry oxygen and the products are collected. They are collected to a temperature of -210C and the ice is removed and has a mass of 5.15g. The remainng gas has a pressure of 744 torr and a volume of 7.76L. What is the empirical formula and write a balance equation for this reaction including states of matter.
To determine the empirical formula and write a balanced equation for this reaction, we need to analyze the given information.
First, let's list the given data:
Mass of the initial sample = 5.15g
Volume of the initial gas = 785ml
Pressure of the initial gas = 1522 torr
Temperature of the initial gas = 280°C
Temperature of the collection chamber = -210°C
Mass of the ice collected = 5.15g
Pressure of the remaining gas = 744 torr
Volume of the remaining gas = 7.76L
Now, let's break down the steps to find the empirical formula and write a balanced equation:
Step 1: Determine the number of moles of the initial gas
To find the number of moles, we use the ideal gas equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the given temperature from Celsius to Kelvin:
T(in Kelvin) = T(in °C) + 273.15
T = 280°C + 273.15 = 553.15 K
Next, convert the given volume of the initial gas from ml to liters:
V = 785 ml ÷ 1000 = 0.785 L
Now, we can plug in the values into the ideal gas equation to calculate the number of moles:
n = (PV) / (RT)
n = (1522 torr * 0.785 L) / (0.0821 L·atm/mol·K * 553.15 K)
Calculate the value of n.
Step 2: Calculate the number of moles of carbon and hydrogen in the initial sample
Since the combustion reaction involves carbon and hydrogen, we need to identify the number of moles of carbon and hydrogen present in the initial sample. To do this, we need to determine the mass of carbon and hydrogen individually.
The total mass of the initial sample is given as 5.15g, and we know that carbon and hydrogen are the only elements present. Since the molar mass of carbon is approximately 12 g/mol and the molar mass of hydrogen is approximately 1 g/mol, we can use these values to find the number of moles of carbon and hydrogen.
Let's assume the number of moles of carbon is x and the number of moles of hydrogen is y.
Using the molar mass, we can write two equations:
12x + 1y = 5.15g (equation 1)
x + y = n (equation 2)
Note: We obtained 'n' (number of moles) in Step 1.
Solve these equations simultaneously to obtain the values of x (moles of carbon) and y (moles of hydrogen).
Step 3: Determine the mole ratio and empirical formula
After obtaining the moles of carbon and hydrogen, calculate their mole ratio by dividing each by the smaller value.
By simplifying the ratio if possible, we can determine the empirical formula.
Step 4: Write the balanced equation for the combustion reaction
The balanced equation for the combustion of carbon and hydrogen in the presence of oxygen will depend on the empirical formula derived in the previous step. The reaction will involve the complete combustion of the empirical formula with oxygen.
Therefore, once you determine the empirical formula, you can use it to write the balanced equation by ensuring that the number of atoms of each element is equal on both sides of the equation.
Be sure to include the states of matter (g for gas, l for liquid, s for solid, aq for aqueous solution) when writing the balanced equation.
Following these steps, you should be able to determine the empirical formula and write a balanced equation for this reaction.