What is the volume of #H_2# generated by reacting 4.33g of #Zn# with excess #H_2SO_4# at 38°C and 760 torr?
Zinc metal will react with dilute sulfuric acid to produce zinc sulfate,
The balanced chemical equation for this single replacement reaction looks like this
#"Zn"_text((s]) + "H"_2"SO"_text(4(aq]) -> "ZnSO"_text(4(aq]) + "H"_text(2(g]) uarr#
Notice that you have a
In your case, you know that the sulfuric acid is in excess, which means that zinc metal acts as a limiting reagent, i.e. it will be completely consumed by the reaction.
Use zinc metal's molar mass to determine how many moles you have in that
#4.33 color(red)(cancel(color(black)("g"))) * "1 mole Zn"/(65.38color(red)(cancel(color(black)("g")))) = "0.06623 moles Zn"#
This means that the reaction produced
Now, in order to determine the volume this much hydrogen gas occupies under those conditions for pressure and temperature, you must use the ideal gas law equation, which looks like this
#color(blue)(PV = nRT)" "#, where
It's important to notice here that the units given to you for pressure and temperature do not match those used in the expression of the universal gas constant.
This means that you have to convert these units from torr to atm, and from degrees Celsius to Kelvin, respectively.
So, rearrange the ideal gas law equation to solve for
#V = (nRT)/P#
#V = (0.06623 color(red)(cancel(color(black)("moles"))) * 0.0821(color(red)(cancel(color(black)("atm"))) * "L")/(color(red)(cancel(color(black)("moles"))) * color(red)(cancel(color(black)("K")))) * (273.15 + 38)color(red)(cancel(color(black)("K"))))/(760/760color(red)(cancel(color(black)("atm"))))#
#V = "1.692 L"#
Rounded to two sig figs, the number of sig figs you have for the pressure and temperature of the gas, the answer will be
#V = color(green)("1.7 L")#
State the Equation
Zinc's only common oxidation state is
Calculating Moles of
First, calculate the moles of
Next, calculate the moles of
Calculating Volume of
In order to find the volume of space occupied by the calculated number of moles of hydrogen gas at the stated conditions, we must consult the ideal gas equation:
#"p"#is pressure in pascals ( #"Pa"#) #"V"#is volume in cubic metres ( #"m"^3#) #"n"#is the number of moles #"R"#is the gas constant = #8.314# #"T"#is the temperature in Kelvin ( #"K"#)
First, convert the given data into workable units:
#1"torr" ~~ 133.322"Pa", :. 760"torr" = 101325"Pa"# #1^@"C" = 274.15"K", :. 38^@"C" = 311.15"K"#
Next, rearrange the equation to solve for volume:
Finally, substitute in your values and solve the equation:
Another useful unit that is probably suitable to use in this situation is the cubic decimetre (