How many grams of potassium chlorate decompose to potassium chloride and 797 mL of O2 at 128 degrees Celsius and 747 torr? 2KClO3 (s) = 2KCl (s) + 3O2 (g)

Question

Wyatt Atkins · Accepted Answer

#1.95# #"g KClO"_3#

We're asked to find the mass, in #"g"#, of #"KClO"_3# that decomposes to give a certain amount of #"O"_2#.

Let's use the ideal gas equation to find the moles of #"O"_2# that form.

#P = 747cancel("torr")((1color(white)(l)"atm")/(760cancel("torr"))) = 0.983# #"atm"#

#V= 797cancel("mL")((1color(white)(l)"L")/(10^3cancel("mL"))) = 0.797# #"L"#

#T = 128^"o""C" + 273 = 401# #"K"#

Entering values that are known, we have

#n = (PV)/(RT) = ((0.983cancel("atm"))(0.797cancel("L")))/((0.082057(cancel("L")•cancel("atm"))/("mol"•cancel("K")))(401cancel("K"))) = 0.0238# #"mol O"_2#

Now, we'll use the coefficients of the chemical equation to find the relative number of moles of #"KClO"_3# that reacted:

#0.0238cancel("mol O"_2)((2color(white)(l)"mol KClO"_3)/(3cancel("mol O"_2))) = 0.0159# #"mol KClO"_3#

Finally, we'll use the molar mass of potassium chlorate (#122.55# #"g/mol"#) to find the number of grams that reacted:

#0.0159cancel("mol KClO"_3)((122.55color(white)(l)"g KClO"_3)/(1cancel("mol O"_2))) = color(blue)(1.95# #color(blue)("g KClO"_3#

Mateo Aguilar · Answer

undefined To solve this problem, we need to use the ideal gas law to find the number of moles of oxygen gas produced. Then, we can use the stoichiometry of the reaction to determine the amount of potassium chlorate that decomposes.

1. Use the ideal gas law to find the number of moles of oxygen gas (O2) produced:
PV = nRT
where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)

First, convert the temperature to Kelvin:
T = 128°C + 273.15 = 401.15 K

Now, convert the pressure from torr to atm:
747 torr ÷ 760 torr/atm = 0.9829 atm

Plug in the values into the ideal gas law equation:
(0.9829 atm)(0.797 L) = n(0.0821 L.atm/mol.K)(401.15 K)

Solve for n (number of moles of O2).

2. Use the stoichiometry of the reaction to determine the amount of potassium chlorate (KClO3) that decomposes:
From the balanced equation, we see that 3 moles of O2 are produced for every 2 moles of KClO3 decomposed.

Calculate the number of moles of KClO3 required to produce the number of moles of O2 found in step 1.

3. Convert moles of KClO3 to grams using its molar mass.

This will give you the grams of potassium chlorate that decompose to produce the given volume of oxygen gas at the specified conditions.