What is the temperature of 0.80 mol of a gas stored in a 275 mL cylinder at 175 kPa?

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What is the temperature of 0.80 mol of a gas stored in a 275 mL cylinder at 175 kPa?

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Answer 1 · 2017-06-01T11:57:56

$7.24$ $7.24$ $K$ $"K"$

Explanation:

First, let's express pressure $P$ $P$ in $Pa$ $"Pa"$ and volume $V$ $V$ in $m^{3}$ $"m"^(3)$ :

$\Rightarrow P = 175$ $Rightarrow P = 175$ $kPa$ $"kPa"$

$\Rightarrow P = 1.75 \times 10^{5}$ $Rightarrow P = 1.75 times 10^(5)$ $Pa$ $"Pa"$

$and$ $"and"$

$\Rightarrow V = 275$ $Rightarrow V = 275$ $ml$ $"ml"$

$\Rightarrow V = 2.75 \times 10^{- 4}$ $Rightarrow V = 2.75 times 10^(- 4)$ $m^{3}$ $"m"^(3)$

Then, let's solve the ideal gas law $P V = n R T$ $P V = n R T$ for temperature $T$ $T$ :

$\Rightarrow P V = n R T$ $Rightarrow P V = n R T$

$\Rightarrow T = \frac{P V}{n R}$ $Rightarrow T = frac(P V)(n R)$

Substituting the appropriate values into the equation:

$\Rightarrow T = \frac{1.75 \times 10^{5} \times 2.75 \times 10^{- 4}}{0.80 \times 8.314}$ $Rightarrow T = frac(1.75 times 10^(5) times 2.75 times 10^(- 4))(0.80 times 8.314)$ $K$ $"K"$

$\Rightarrow T = \frac{48.125}{6.6512}$ $Rightarrow T = frac(48.125)(6.6512)$ $K$ $"K"$

$therefore T approx 7.24$ $"K"$

Therefore, the temperature is around $7.24$ $"K"$ .

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What is the temperature of 0.80 mol of a gas stored in a 275 mL cylinder at 175 kPa?

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