A gas has a volume of 146 cm3 at 18°C and 0.971 atm. What is its volume at STP?

Question

ScanSolve AI Tutor · Accepted Answer

To find the volume of the gas at Standard Temperature and Pressure (STP), we will use the Combined Gas Law. STP is defined as $0^\circ\text{C}$ (273 K) and $1 \text{ atm}$ .

List the initial conditions ( $P_1, V_1, T_1$ ).
- Initial volume ( $V_1$ ) = $146 \text{ cm}^3$
- Initial temperature ( $T_1$ ) = $18^\circ\text{C}$
- Initial pressure ( $P_1$ ) = $0.971 \text{ atm}$
Convert the initial temperature to Kelvin.
$T_1 = 18^\circ\text{C} + 273.15 = 291.15 \text{ K}$
List the final conditions at STP ( $P_2, T_2$ ).
- Standard temperature ( $T_2$ ) = $0^\circ\text{C} = 273.15 \text{ K}$
- Standard pressure ( $P_2$ ) = $1 \text{ atm}$
- Final volume ( $V_2$ ) = ?
Apply the Combined Gas Law.
The Combined Gas Law states:
$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$
Rearrange the formula to solve for $V_2$ :
$V_2 = \frac{P_1V_1T_2}{P_2T_1}$
Substitute the values and calculate $V_2$ .
$V_2 = \frac{(0.971 \text{ atm}) \times (146 \text{ cm}^3) \times (273.15 \text{ K})}{(1 \text{ atm}) \times (291.15 \text{ K})}$ $V_2 = \frac{38758.9999 \text{ cm}^3}{291.15}$ $V_2 \approx 133.12 \text{ cm}^3$
Rounding to three significant figures:
$V_2 \approx 133 \text{ cm}^3$
The volume of the gas at STP is:
$\text{133 cm}^3$

A gas has a volume of 146 cm3 at 18°C and 0.971 atm. What is its volume at STP?

Answer

Step-by-step solution

List the initial conditions ( $P_1, V_1, T_1$ ).

Convert the initial temperature to Kelvin.

List the final conditions at STP ( $P_2, T_2$ ).

Apply the Combined Gas Law.

Substitute the values and calculate $V_2$ .

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More Physics Questions

A gas has a volume of 146 cm3 at 18°C and 0.971 atm. What is its volume at STP?

Answer

Step-by-step solution

List the initial conditions (P1,V1,T1P_1, V_1, T_1P1​,V1​,T1​).

Convert the initial temperature to Kelvin.

List the final conditions at STP (P2,T2P_2, T_2P2​,T2​).

Apply the Combined Gas Law.

Substitute the values and calculate V2V_2V2​.

Try one yourself

Still stuck on this one?

More Physics Questions

List the initial conditions ( $P_1, V_1, T_1$ ).

List the final conditions at STP ( $P_2, T_2$ ).

Substitute the values and calculate $V_2$ .