How many moles are in a gas in 890mL at 21 °C and 750 mmHg?

Question

Mateo Aguilar · Accepted Answer

#n="0.036 mol"# Use the ideal gas law. The formula is #PV=nRT#, where #P# is pressure, #V# is volume, #n# is moles, #R# is the gas constant, and #T# is the Kelvin temperature. Given/Known #P="750 mmHg"="750 Torr"# #V=890cancel"mL"xx(1"L")/(1000cancel"mL")="0.89 L"# #R="62.363577 L Torr K"^(-1) "mol"^(-1)# https://tutor.hix.ai #T="21"^@"C"+273.15"=294 K"# Unknown #n# Solution Rearrange the formula to isolate #n#. Substitute the given/known values into the formula and solve. #PV=nRT# #n=(PV)/(RT)# #n=(750cancel"Torr" * 0.89cancel"L")/((62.363577 cancel"L" cancel"Torr" cancel"K"^(-1)" mol"^(-1))xx(294cancel"K"))="0.036 mol"# rounded to two significant figures

Jose Ayala · Answer

undefined To find the number of moles of a gas, you can use the ideal gas law equation:

$$PV = nRT$$

Where:
- $P$ is the pressure in atmospheres (atm)
- $V$ is the volume in liters (L)
- $n$ is the number of moles
- $R$ is the ideal gas constant ($0.0821$ L·atm/mol·K)
- $T$ is the temperature in Kelvin (K)

First, convert the volume from milliliters (mL) to liters (L): $890 \text{ mL} = 0.890 \text{ L}$

Then, convert the temperature from Celsius to Kelvin: $21 °C + 273.15 = 294.15 \text{ K}$

Plug in the values into the ideal gas law equation:

$$750 \text{ mmHg} \times 1 \text{ atm} / 760 \text{ mmHg} = 0.987 \text{ atm}$$

$PV = nRT$ becomes $0.987 \text{ atm} \times 0.890 \text{ L} = n \times 0.0821 \text{ L·atm/mol·K} \times 294.15 \text{ K}$

Solve for $n$, the number of moles:

$0.877 \text{ atm·L} = n \times 24.189 \text{ L·atm/mol}$

$n = \frac{0.877 \text{ atm·L}}{24.189 \text{ L·atm/mol}}$

$n \approx 0.036 \text{ moles}$

So, there are approximately 0.036 moles of gas in the given conditions.