Each of the small metal canisters shown in the photograph contains 0.36 moles of carbon dioxide. The contents of one canister were released into a flat bicycle tube. The gas inflated the tube to a volume of 1.0 × 10^{-3} m^{3} at a temperature of 293 K. Calculate the pressure of the gas inside the tube correct to two significant figures.

Leaving Cert Chemistry Gas Laws & Properties: Each of the small metal canister

Each of the small metal canisters shown in the photograph contains 0.36 moles of carbon dioxide - Leaving Cert Chemistry - Question f - 2020

Question f

Each of the small metal canisters shown in the photograph contains 0.36 moles of carbon dioxide. The contents of one canister were released into a flat bicycle tube.... show full transcript

Worked Solution & Example Answer:Each of the small metal canisters shown in the photograph contains 0.36 moles of carbon dioxide - Leaving Cert Chemistry - Question f - 2020

Step 1

Using the Ideal Gas Law: $PV = nRT$

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Answer

To calculate the pressure of the gas inside the tube, we start by using the Ideal Gas Law, given by:

$PV = nRT$

where:

$P$ is the pressure,
$V$ is the volume,
$n$ is the number of moles of gas,
$R$ is the universal gas constant (approximately 8.31 J/(mol·K)), and
$T$ is the temperature in Kelvin.

Step 2

Substituting Values

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Answer

We have:

$n = 0.36$ moles of $CO_2$ ,
$V = 1.0 \times 10^{-3} \, m^3$ ,
$R = 8.31 \, J/(mol \, K)$ ,
$T = 293 \, K$ .

Substituting these values into the Ideal Gas Law:

$P \times (1.0 \times 10^{-3}) = 0.36 \times 8.31 \times 293$

Step 3

Calculating Pressure

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Answer

Now we can calculate the right-hand side:

$0.36 \times 8.31 \times 293 = 87654.81 \, Pa$

Thus, we rearrange the formula to solve for $P$ :

$P = \frac{87654.81}{1.0 \times 10^{-3}} = 8.765481 \times 10^7 \, Pa$

To express this to two significant figures, the pressure of the gas inside the tube is:

$P \approx 8.8 \times 10^5 \, Pa$

Each of the small metal canisters shown in the photograph contains 0.36 moles of carbon dioxide - Leaving Cert Chemistry - Question f - 2020

Worked Solution & Example Answer:Each of the small metal canisters shown in the photograph contains 0.36 moles of carbon dioxide - Leaving Cert Chemistry - Question f - 2020

Using the Ideal Gas Law: $PV = nRT$

Substituting Values

Calculating Pressure

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