# What steps can you do to figure out a chemical reaction from Dalton's gas law if given only the data? P atm= 656.7, T h20= 27 C, V initial= 0.30 mL, V final = 17.05 mL and mass of Alka-seltzer 0.123g.

Mar 5, 2015

You're describing a classic reaction used to produce $C {O}_{2}$ gas.

First thing first, I think your pressure is actually 656.7 mmHg, since 656.7 atm is a very unreasonable figure, to say the least.

Here's what basically happens. Alka-seltzer contains sodium bicarbonate, or $N a H C {O}_{3}$, and citric acid, or ${C}_{6} {H}_{8} {O}_{7}$. When placed in water, the sodium bicarbonate reacts with the citric acid and produces water, carbon dioxide, and one of citric acid's salts, trisodium citrate to be exact.

Dalton's law of partial pressures comes in handy because the carbon dioxide gas that is collected over water is mixed with water vapor. You'll use it to calculate the actual pressure of the carbon dioxide.

The change in volume will be the volume occupied by the carbon dioxide and water vapor; in your case, the volume went from 0.30 mL to 17.05 mL.

The temperature of the water is given so that you can use its vapor pressure at that respective temperature.

So, I'll show you an example of what the reaction could be

$3 N a H C {O}_{3 \left(s\right)} + {C}_{6} {H}_{8} {O}_{7 \left(a q\right)} \to 3 C {O}_{2 \left(g\right)} + N {a}_{3} {C}_{6} {H}_{5} {O}_{7 \left(a q\right)} + 3 {H}_{2} {O}_{\left(l\right)}$

So, let's focus on the produced $C {O}_{2}$. The total pressure will be

${P}_{\text{total") = P_(CO_2) + P_("water vapor}}$

At ${27}^{\circ} \text{C}$, water has a vapor pressure of 26.66 mmHg, which means that

P_(CO_2) = P_("total") - P_("water vapor") = ("656.7" - "26.66")"mmHg" = "630.04 mmHg"

Its volume will be

V_(CO_2) = V_("final") - V_("initial") = "17.05 mL" - "0.30 mL" = "16.75 mL"

Use the ideal gas law equation to solve for the number of moles of $C {O}_{2}$ produced

$P V = n R T \implies n = \frac{P V}{R T} = \left(\frac{630.04}{760} \text{atm" * 16.75 * 10^(-3)"L")/(0.082("atm" * "L")/("mol" * "K") * (273.15 + 27)"K}\right)$

${n}_{C {O}_{2}} = \text{0.0005642 moles }$ $C {O}_{2}$

The mass of carbon dioxide produced will be

$\text{0.0005642 moles" * "44.0 g"/"1 mole" = "0.0248 g } C {O}_{2}$

Use the mole ratios that exist between carbon dioxide and sodium bicarbonate (1:1), and between carbon dioxide and citric acid (3:1), to determine how much of each compound was present in the Alka-seltzer tablet.

$\text{0.0005642 moles" CO_2 * ("3 moles"NaHCO_3)/("3 moles"CO_2) = "0.0005642 moles} N a H C {O}_{3}$

and

$\text{0.0005642 moles" CO_2 * ("1 mole"C_6H_8O_7)/("3 moles"CO_2) = "0.0001881 moles} {C}_{6} {H}_{8} {O}_{7}$

Using the compounds' molar masses will get you to the masses that reacted

$\text{0.0005642 moles"NaHCO_3 * "84.0 g"/"1 mole" = "0.0474 g} N a H C {O}_{3}$

and

$\text{0.0001881 moles"C_6H_8O_7 * "192.12 g"/"1 mole" = "0.0361 g} {C}_{6} {H}_{8} {O}_{7}$

Your tablet has a weight of 0.123 g, out of which 0.0474 g will be sodium bicarbonate and 0.0361 g will be citric acid.

So, as a conclusion:

When you place a 0.123-g tablet of Alka-seltzer in water at 27 degrees Celsius, the reaction that takes place between sodium bicarbonate and citric acid will produce 0.0248 g of carbon dioxide under your specific conditions of pressure and temperature.

The volume occupied by the gas will be 16.75 mL.

SIDE NOTE I'm not exactly sure you are interested in all the things I wrote, but I wanted to show you exactly how it all comes together.